Tetsu Shimomura

Last Updated :2024/09/06

Affiliations, Positions
Graduate School of Humanities and Social Sciences, Professor
E-mail
tshimohiroshima-u.ac.jp

Basic Information

Academic Degrees

  • Doctor of Philosophy, Hiroshima University
  • Master, Hiroshima University

Research Fields

  • Mathematical and physical sciences;Mathematics;Basic analysis

Research Keywords

  • Sobolev functions

Educational Activity

Course in Charge

  1. 2024, Undergraduate Education, 1Term, Computer Practice
  2. 2024, Undergraduate Education, 2Term, Computer Practice
  3. 2024, Undergraduate Education, 2Term, Research Methods in Analysis I
  4. 2024, Undergraduate Education, 4Term, Study of Instructional Materials in Analysis
  5. 2024, Undergraduate Education, Second Semester, Graduation Thesis
  6. 2024, Undergraduate Education, First Semester, Study of Instructional Materials in Analysis Education
  7. 2024, Undergraduate Education, Second Semester, Practical Seminar for the Teaching Profession
  8. 2024, Graduate Education (Master's Program) , First Semester, Special Study in Mathematics Education A
  9. 2024, Graduate Education (Master's Program) , Second Semester, Special Study in Mathematics Education A
  10. 2024, Graduate Education (Master's Program) , 3Term, Basic Course in Teaching Material Design for Science and Culture (Mathematics) b
  11. 2024, Graduate Education (Doctoral Program) , First Semester, Special Study
  12. 2024, Graduate Education (Doctoral Program) , Second Semester, Special Study

Research Activities

Academic Papers

  1. Trudinger-type inequalities for variable Riesz potentials of functions in Musielak-Orlicz-Morrey spaces over metric measure spaces, MATHEMATISCHE NACHRICHTEN, 297(4), 1248-1274, 202404
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  2. Vanishing exponential integrability for Riesz potentials in Morrey-Orlicz spaces, MATHEMATISCHE NACHRICHTEN, 297(1), 110-125, 202401
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  3. Sobolev type inequalities for fractional maximal functions and Riesz potentials in Morrey spaces of variable exponent on half spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 73(4), 1201-1217, 202312
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  4. Integrability for Hardy operators of double phase, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 42(3-4), 375-402, 2023
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  5. Generalized solution of the double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces, HIROSHIMA MATHEMATICAL JOURNAL, 53(3), 359-372, 202311
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  6. Hardy-Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces, ACTA MATHEMATICA HUNGARICA, 171(2), 221-240, 202312
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  7. Continuity of Generalized Riesz Potentials for Double Phase Functionals with Variable Exponents over Metric Measure Spaces, TAIWANESE JOURNAL OF MATHEMATICS, 27(4), 813-832, 202308
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  8. VANISHING MORREY INTEGRABILITY FOR RIESZ POTENTIALS IN MORREY-ORLICZ SPACES, MATHEMATICA SCANDINAVICA, 129(2), 374-400, 2023
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  9. Continuity of Riesz potentials for double phase functionals with variable exponents, PUBLICATIONES MATHEMATICAE DEBRECEN, 103(1-2), 171-186, 2023
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  10. BOUNDEDNESS OF INTEGRAL OPERATORS OF DOUBLE PHASE, MATHEMATICAL INEQUALITIES & APPLICATIONS, 26(3), 703-716, 202307
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  11. Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 68(10), 1694-1714, 20231003
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  12. Sobolev's inequality in Musielak-Orlicz-Morrey spaces of an integral form, MATHEMATISCHE NACHRICHTEN, 296(9), 4152-4168, 202309
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  13. Hardy-Sobolev inequalities for double phase functionals, HOKKAIDO MATHEMATICAL JOURNAL, 52(2), 331-352, 202306
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  14. ★, Sobolev's Inequality for Musielak-Orlicz-Sobolev Functions, RESULTS IN MATHEMATICS, 78(3), 202306
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  15. ★, Hardy-Littlewood-Sobolev Theorem for Variable Riesz Potentials, RESULTS IN MATHEMATICS, 78(3), 202306
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  16. Trudinger's Inequality on Musielak-Orlicz-Morrey Spaces Over Non-doubling Metric Measure Spaces, MEDITERRANEAN JOURNAL OF MATHEMATICS, 20(3), 202306
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  17. Generalized fractional maximal operators on Musielak-Orlicz-Morrey spaces, POSITIVITY, 27(2), 202304
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  18. RIESZ POTENTIALS AND SOBOLEV-TYPE INEQUALITIES IN ORLICZ-MORREY SPACES OF AN INTEGRAL FORM, CZECHOSLOVAK MATHEMATICAL JOURNAL, 73(1), 263-276, 202303
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  19. Sobolev-Type Inequalities on Musielak-Orlicz-Morrey Spaces of an Integral Form, BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 46(1), 202301
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  20. TRUDINGER-TYPE INEQUALITIES IN MUSIELAK-ORLICZ SPACES, HOUSTON JOURNAL OF MATHEMATICS, 48(3), 479-497, 2022
  21. Boundary growth of Sobolev functions of monotone type for double phase functionals, ANNALES FENNICI MATHEMATICI, 47(1), 23-37, 2022
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  22. Sobolev and Trudinger inequalities in weighted Morrey spaces for double phase functionals, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 41(3-4), 439-466, 2022
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  23. Generalized fractional integral operators on variable exponent Morrey type spaces over metric measure spaces, PORTUGALIAE MATHEMATICA, 79(3-4), 265-282, 2022
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  24. Compact embeddings for Sobolev spaces of two variable exponents, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 67(12), 3009-3022, 20221202
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  25. HARDY-SOBOLEV INEQUALITY IN HERZ SPACES, TOHOKU MATHEMATICAL JOURNAL, 74(2), 287-300, 2022
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  26. GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON VARIABLE EXPONENT MORREY SPACES OF AN INTEGRAL FORM, ACTA MATHEMATICA HUNGARICA, 167(1), 201-214, 202206
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  27. ★, Boundedness of fractional integral operators in Herz spaces on the hyperplane, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 45(14), 8631-8654, 20220930
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  28. On Sobolev-type Inequalities on Morrey Spaces of an Integral Form, TAIWANESE JOURNAL OF MATHEMATICS, 26(4), 831-845, 202208
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  29. HARDY AND SOBOLEV INEQUALITIES FOR DOUBLE PHASE FUNCTIONALS ON THE UNIT BALL, MATHEMATICAL INEQUALITIES & APPLICATIONS, 25(2), 319-333, 202204
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  30. Sobolev-type inequalities on variable exponent Morrey spaces of an integral form, RICERCHE DI MATEMATICA, 71(1), 189-204, 202206
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  31. Maximal and Riesz Potential Operators in Double Phase Lorentz Spaces of Variable Exponents, MATHEMATICAL NOTES, 111(5-6), 729-735, 202206
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  32. Sobolev's inequality in central Herz-Morrey-Musielak-Orlicz spaces over metric measure spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 67(5), 1154-1185, 20220504
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  33. HARDY-SOBOLEV INEQUALITIES IN THE HALF-SPACE FOR DOUBLE PHASE FUNCTIONALS, ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 51(6), 2159-2169, 202112
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  34. Hardy-Sobolev inequality for Sobolev functions in central Herz-Morrey spaces, MATHEMATISCHE NACHRICHTEN, 294(6), 1148-1159, 202106
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  35. Nonhomogeneous central Morrey-type spaces in L-P(.) and weak estimates for the maximal and Riesz potential operators, KYOTO JOURNAL OF MATHEMATICS, 62(1), 133-150, 202204
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  36. TRUDINGER-TYPE INEQUALITIES ON MUSIELAK-ORLICZ-MORREY SPACES OF AN INTEGRAL FORM, MATHEMATICA SCANDINAVICA, 128(1), 78-108, 2022
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  37. CONTINUITY OF GENERALIZED RIESZ POTENTIALS FOR DOUBLE PHASE FUNCTIONALS WITH VARIABLE EXPONENTS, GLASNIK MATEMATICKI, 56(2), 329-341, 202112
  38. Sobolev embeddings in grand Morrey spaces, MATHEMATISCHE NACHRICHTEN, 294(12), 2367-2381, 202112
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  39. BOUNDARY LIMITS OF MONOTONE SOBOLEV FUNCTIONS ON METRIC SPACES, OSAKA JOURNAL OF MATHEMATICS, 58(1), 135-147, 202101
  40. Weak Estimates for the Maximal and Riesz Potential Operators in Central Herz-Morrey Spaces on the Unit Ball, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 40(2), 183-207, 2021
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  41. Boundedness of maximal operator, Hardy operator and Sobolev's inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces, HIROSHIMA MATHEMATICAL JOURNAL, 51(1), 13-55, 202103
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  42. HERZ-MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING 1 AND DOUBLE PHASE FUNCTIONALS, NAGOYA MATHEMATICAL JOURNAL, 242, 1-34, 202106
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  43. Trudinger's Inequality for Double Phase Functionals with Variable Exponents, CZECHOSLOVAK MATHEMATICAL JOURNAL, 71(2), 511-528, 202106
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  44. SOBOLEV'S INEQUALITY FOR MUSIELAK-ORLICZ-MORREY SPACES OVER METRIC MEASURE SPACES, JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 110(3), 371-385, 202106
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  45. Hardy-Sobolev inequalities in the unit ball for double phase functionals, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501(1), 20210901
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  46. Boundedness of fractional maximal operators for double phase functionals with variable exponents, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501(1), 20210901
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  47. THE DOUBLE OBSTACLE PROBLEM FORMUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES, TOHOKU MATHEMATICAL JOURNAL, 73(1), 119-136, 2021
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  48. CONTINUITY OF GENERALIZED RIESZ POTENTIALS FOR DOUBLE PHASE FUNCTIONALS, MATHEMATICAL INEQUALITIES & APPLICATIONS, 24(3), 715-723, 202107
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  49. On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 64(1), 75-90, 202103
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  50. ★, Fractional Maximal Operator on Musielak-Orlicz Spaces Over Unbounded Quasi-Metric Measure Spaces, RESULTS IN MATHEMATICS, 76(4), 202112
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  51. HARDY-SOBOLEV INEQUALITIES FOR SOBOLEV FUNCTIONS IN CENTRAL HERZ-MORREY SPACES ON THE UNIT BALL, ANNALES FENNICI MATHEMATICI, 46(2), 1031-1052, 2021
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  52. BOUNDARY GROWTH OF SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 45, 279-292, 2020
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  53. SOBOLEV'S THEOREM FOR DOUBLE PHASE FUNCTIONALS, MATHEMATICAL INEQUALITIES & APPLICATIONS, 23(1), 17-33, 202001
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  54. ★, Generalized Riesz potentials of functions in Morrey spaces L-(1,L-phi;kappa)(G) over non-doubling measure spaces, FORUM MATHEMATICUM, 32(2), 339-359, 202003
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  55. Sobolev's Inequality for Riesz Potentials of Functions in Musielak-Orlicz-Morrey Spaces Over Non-doubling Metric Measure Spaces, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 63(2), 287-303, 202006
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  56. Campanato-Morrey spaces for the double phase functionals with variable exponents, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 197, 202008
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  57. Hardy and Sobolev inequalities in the half space, ACTA MATHEMATICA HUNGARICA, 161(1), 230-244, 202006
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  58. WEAK ESTIMATES FOR THE MAXIMAL AND RIESZ POTENTIAL OPERATORS ON NON-HOMOGENEOUS CENTRAL MORREY TYPE SPACES IN L-1 OVER METRIC MEASURE SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 45, 1187-1207, 2020
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  59. Growth properties for generalized Riesz potentials of functions satisfying Orlicz conditions, MATHEMATISCHE NACHRICHTEN, 293(6), 1156-1173, 202006
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  60. Boundedness of the maximal and potential operators in Herz-Morrey type spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 65(9), 1575-1589, 20200901
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  61. Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces, GEORGIAN MATHEMATICAL JOURNAL, 27(3), 433-439, 202009
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  62. GAGLIARDO-NIRENBERG INEQUALITY FOR GENERALIZED RIESZ POTENTIALS OF FUNCTIONS IN MUSIELAK-ORLICZ SPACES OVER QUASI-METRIC MEASURE SPACES, COLLOQUIUM MATHEMATICUM, 161(1), 51-66, 2020
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  63. BOUNDARY LIMITS OF MONOTONE SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS, OSAKA JOURNAL OF MATHEMATICS, 57(4), 819-826, 202010
  64. BOUNDEDNESS OF MAXIMAL OPERATORS ON HERZ SPACES WITH RADIAL VARIABLE EXPONENT, TOHOKU MATHEMATICAL JOURNAL, 72(3), 335-348, 2020
  65. Campanato-Morrey spaces for the double phase functionals, REVISTA MATEMATICA COMPLUTENSE, 33(3), 817-834
  66. Duality of central Herz-Morrey-Musielak-Orlicz spaces of variable exponents, COLLECTANEA MATHEMATICA, 70(1), 117-151, 201901
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  67. ★, Sobolev's inequality for double phase functionals with variable exponents, FORUM MATHEMATICUM, 31(2), 517-527, 201903
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  68. OBSTACLE PROBLEM FOR MUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES, TOHOKU MATHEMATICAL JOURNAL, 71(1), 53-68, 2019
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  69. BOUNDARY GROWTH OF GENERALIZED RIESZ POTENTIALS ON THE UNIT BALL IN THE VARIABLE SETTINGS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 44, 125-140, 2019
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  70. Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L-1 Over Metric Measure Spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 69(1), 207-223, 201903
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  71. Lindelof theorems for monotone Sobolev functions in Orlicz spaces on uniform domains, MATHEMATISCHE NACHRICHTEN, 292(4), 793-804, 201904
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  72. OPTIMAL ESTIMATES FOR THE FRACTIONAL HARDY OPERATOR ON VARIABLE EXPONENT LEBESGUE SPACES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 22(2), 445-462, 201904
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  73. ROUNDEDNESS OF GENERALIZED RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES L-(1,L-phi:kappa) (G) OVER NON-DOUBLING MEASURE SPACES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 22(2), 577-599, 201904
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  74. MAXIMAL OPERATOR ON ORLICZ SPACES OF TWO VARIABLE EXPONENTS OVER UNBOUNDED QUASI-METRIC MEASURE SPACES, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 147(7), 2877-2885, 201907
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  75. Weak estimates for the maximal and Riesz potential operators in non-homogeneous central Herz-Morrey spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 64(9), 1437-1456, 20190902
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  76. Sobolev inequalities for Musielak-Orlicz spaces, MANUSCRIPTA MATHEMATICA, 155(1-2), 209-227, 201801
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  77. SOBOLEV'S INEQUALITIES FOR HERZ-MORREY-ORLICZ SPACES ON THE HALF SPACE, MATHEMATICAL INEQUALITIES & APPLICATIONS, 21(2), 433-453, 201804
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  78. A remark on modified Morrey spaces on metric measure spaces, HOKKAIDO MATHEMATICAL JOURNAL, 47(1), 1-15, 201802
  79. GROWTH PROPERTIES OF POTENTIALS IN CENTRAL MORREY-ORLICZ SPACES ON THE UNIT BALL, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 43(1), 21-46, 2018
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  80. VARIABLE EXPONENT WEIGHTED NORM INEQUALITY FOR GENERALIZED RIESZ POTENTIALS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 43(1), 563-577, 2018
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  81. ★, Boundary Behavior of Monotone Sobolev Functions in Orlicz Spaces on John Domains in a Metric Space, JOURNAL OF GEOMETRIC ANALYSIS, 28(2), 1233-1244, 201804
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  82. Generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces, GEORGIAN MATHEMATICAL JOURNAL, 25(2), 303-311, 201806
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  83. Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball, COLLECTANEA MATHEMATICA, 69(3), 377-394, 201809
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  84. Maximal and Riesz Potential Operators on Musielak-Orlicz Spaces Over Metric Measure Spaces, INTEGRAL EQUATIONS AND OPERATOR THEORY, 90(6), 201812
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  85. Sobolev's inequality for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces, MATHEMATISCHE NACHRICHTEN, 291(10), 1547-1562, 201807
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  86. Trudinger's inequality and continuity for Riesz potential of functions in Orlicz spaces of two variable exponents over nondoubling measure spaces, KYOTO JOURNAL OF MATHEMATICS, 57(1), 79-96, 201704
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  87. Boundary limits of monotone Sobolev functions in Musielak-Orlicz spaces on uniform domains in a metric space, KYOTO JOURNAL OF MATHEMATICS, 57(1), 147-164, 201704
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  88. Boundedness of the Generalized Fractional Integral Operators on Generalized Morrey Spaces over Metric Measure Spaces, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 36(2), 159-190, 2017
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  89. Generalized fractional integral operators over non-doubling metric measure spaces, INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 28(7), 534-546, 201707
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  90. Growth properties near the origin for generalized Riesz potentials, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 454(1), 285-302, 2017
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  91. Duality of Non-Homogeneous Central Herz-Morrey-Musielak-Orlicz Spaces, POTENTIAL ANALYSIS, 47(4), 447-460, 2017
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  92. BOUNDEDNESS OF THE MAXIMAL OPERATOR ON MUSIELAK-ORLICZ-MORREY SPACES, TOHOKU MATHEMATICAL JOURNAL, 69(4), 483-495, 2017
  93. Growth properties for Riesz potentials of functions in weighted variable Lp(.) spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 162, 49-75, 201710
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  94. SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN Lp(.) OVER NONDOUBLING MEASURE SPACES, BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 93(1), 128-136, 2016
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  95. Boundedness of Generalized Fractional Integral Operators From the Morrey Space L-1,L-phi(X; mu) to the Campanato Space L-1,L-psi(X; mu) Over Non-doubling Measure Spaces, AZERBAIJAN JOURNAL OF MATHEMATICS, 6(2), 117-127, 201607
  96. SOME NORM INEQUALITIES IN MUSIELAK-ORLICZ SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 41(2), 721-744, 2016
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  97. Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 66(2), 371-394, 2016
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  98. Trudinger's inequality and continuity for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces, KYOTO JOURNAL OF MATHEMATICS, 56(3), 633-653, 201609
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  99. Boundedness of Maximal Operators and Sobolev's Inequality on Non-Homogeneous Central Musielak-Orlicz-Morrey Spaces, MEDITERRANEAN JOURNAL OF MATHEMATICS, 13(5), 3341-3357, 201610
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  100. Growth properties of Musielak-Orlicz integral means for Riesz potentials, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 112, 69-83, 201501
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  101. Boundary limits of monotone Sobolev functions with variable exponent on uniform domains in a metric space, REVISTA MATEMATICA COMPLUTENSE, 28(1), 31-48, 201501
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  102. SOBOLEV AND TRUDINGER TYPE INEQUALITIES ON GRAND MUSIELAK-ORLICZ-MORREY SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 40(1), 403-426, 2015
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  103. Musielak-Orlicz-Sobolev spaces on metric measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 65(2), 435-474, 201506
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  104. Weighted Morrey spaces of variable exponent and Riesz potentials, MATHEMATISCHE NACHRICHTEN, 288(8-9), 984-1002, 201506
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  105. Boundedness of maximal operators and Sobolev's theorem for non-homogeneous central Morrey spaces of variable exponent, HOKKAIDO MATHEMATICAL JOURNAL, 44(2), 185-201, 201506
  106. Problem posing in the upper grades using computers, Mathematical Problem Posing, Springer-Verlag New York, 257-272, 2015
  107. Optimal estimates for the fractional Hardyoperator, STUDIA MATHEMATICA, 227(1), 1-19, 2015
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  108. EXPONENTIAL INTEGRABILITY FOR LOGARITHMIC POTENTIALS OF FUNCTIONS IN GENERALIZED LEBESGUE SPACES L(log L)(q(.)) OVER NON-DOUBLING MEASURE SPACES, TAIWANESE JOURNAL OF MATHEMATICS, 19(6), 1795-1803, 201512
  109. Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces, BULLETIN DES SCIENCES MATHEMATIQUES, 138(2), 225-235, 201403
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  110. Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 106, 1-17, 201409
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  111. Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 64(1), 209-228, 201403
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  112. Sobolev embeddings for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces over non-doubling measure spaces, INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 25(12), 976-991, 20141202
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  113. Hardy's inequality in Musielak-Orlicz-Sobolev spaces, HIROSHIMA MATHEMATICAL JOURNAL, 44(2), 139-155, 201407
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  114. SOBOLEV EMBEDDINGS FOR RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES L-1,L-nu,L- beta 1,L-beta 2(R-n), MATHEMATICAL INEQUALITIES & APPLICATIONS, 17(4), 1399-1414, 201410
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  115. Trudinger's Inequality and Continuity of Potentials on Musielak-Orlicz-Morrey Spaces, POTENTIAL ANALYSIS, 38(2), 515-535, 201302
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  116. ★, Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces, BULLETIN DES SCIENCES MATHEMATIQUES, 137(1), 76-96, 2013
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  117. On the Boundary Limits of Monotone Sobolev Functions in Variable Exponent Orlicz Spaces, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 29(3), 461-470, 201303
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  118. Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces L-(1,L-phi)(G) over Nondoubling Measure Spaces, JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013
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  119. Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 65(2), 633-670, 201304
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  120. Hardy Averaging Operator on Generalized Banach Function Spaces and Duality, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 32(2), 233-255, 2013
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  121. ★, Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents, COLLECTANEA MATHEMATICA, 64(3), 313-350, 201309
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  123. Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponentattaining the value $1$ over non-doubling measure spaces, Journal of Inequalities and Applications, 2013:12, 20130101
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  129. Weighted Sobolev inequality in Musielak-Orlicz space, J. Math. Anal. Appl., 388, 86-97, 20120101
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  132. Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces, ARCHIV DER MATHEMATIK, 98(3), 253-263, 201203
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  133. EXPONENTIAL INTEGRABILITY OF RIESZ POTENTIALS OF ORLICZ FUNCTIONS, ILLINOIS JOURNAL OF MATHEMATICS, 56(2), 507-520, 2012
  134. Iterated maximal functions in variable exponent Lebesgue spaces, MANUSCRIPTA MATHEMATICA, 135(3-4), 381-399, 201107
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  135. Capacity for potentials of functions in Musielak-Orlicz spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 74(17), 6231-6243, 201112
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  136. Hardy's inequality in Orlicz-Sobolev spaces of variable exponent, HOKKAIDO MATHEMATICAL JOURNAL, 40(2), 187-203, 201106
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  137. Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 56(7-9), 671-695, 2011
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  138. ORLICZ-SOBOLEV CAPACITY OF BALLS, ILLINOIS JOURNAL OF MATHEMATICS, 55(2), 543-553, 2011
  139. Sobolev's inequality for Riesz potentials in Orlicz-Musielak spaces, Proceedings of the International Symposium on Banach and Function Spaces III (Kitakyushu, Japan, 2009), 409-419, 2011
  140. Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent, BULLETIN DES SCIENCES MATHEMATIQUES, 134(1), 12-36, 2010
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  141. Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 366(2), 391-417, 20100615
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  142. COMPACT EMBEDDINGS FOR SOBOLEV SPACES OF VARIABLE EXPONENTS AND EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS INVOLVING THE p(x)-LAPLACIAN AND ITS CRITICAL EXPONENT, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 35(1), 115-130, 2010
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  143. SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS, GLASGOW MATHEMATICAL JOURNAL, 52, 227-240, 201005
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  144. Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 62(3), 707-744, 201007
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  145. Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form, MATHEMATISCHE NACHRICHTEN, 283(9), 1336-1352, 201009
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  146. CONTINUITY PROPERTIES FOR RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES OF VARIABLE EXPONENT, MATHEMATICAL INEQUALITIES & APPLICATIONS, 13(1), 99-122, 201001
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  147. WEIGHTED ORLICZ-RIESZ CAPACITY OF BALLS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138(12), 4291-4302, 201012
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  148. Variable exponent spaces on metric measure spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr and Nicolosi (ed.)), 107-121, 2009
  149. Continuity properties of Riesz potentials of Orlicz functions, Tohoku Mathematical Journal, 61(2), 225-240, 20090601
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  151. SOBOLEV'S INEQUALITY FOR RIESZ POTENTIALS OF FUNCTIONS IN NON-DOUBLING MORREY SPACES, OSAKA JOURNAL OF MATHEMATICS, 46(1), 255-271, 200903
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  152. ★, MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 34(2), 503-522, 2009
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  154. Sobolev's inequality for Orlicz-Sobolev spaces of variable exponents, 京都大学数理解析研究所講究録, 1669, 91-102, 2009
  155. An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $L^{1,\nu,\beta}(G)$, Hiroshima Math. J., 38(3), 425-436, 20081101
  156. Lindel\"of theorems for monotone Sobolev functions with variable exponent, Proc. Japan Acad. Ser. A Math. Sci., 84, 25-28, 20080201
  157. Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 60(2), 583-602, 200804
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  158. Lindelof theorems for monotone Sobolev functions with variable exponent, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 84(2), 25-28, 200802
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  159. Integrability of maximal functions for generalized Lebesgue spaces with variable exponent, MATHEMATISCHE NACHRICHTEN, 281(3), 386-395, 2008
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  160. Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(.)log L)q(.), JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 345(1), 70-85, 20080901
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  161. Continuity properties and vanishing exponential integrability of Riesz potentials of Orlicz functions, 1553, 137-148, 2007
  162. Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes, ILLINOIS JOURNAL OF MATHEMATICS, 51(4), 1039-1060, 2007
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  163. ★, Sobolev embeddings for Riesz potential space of variable exponent on metric spaces, Ann. Acad. Sci. Fenn. Math., 31, 495-522, 20060601
  164. Sobolev embeddings for Riesz potential space of variable exponent, Math. Nachr., 279, 1463-1473, 20060401
  165. Sobolev embeddings for variable exponent Riesz potentials on metric spaces {\bf 31} (2006),, Ann. Acad. Sci. Fenn. Math., 31, 495-522, 20060401
  166. Sobolev embedding theorems for variable exponent Riesz potentials, 22, 21-30, 20060401
  167. Numerical computation of cross-coupled algebraic Riccati equations related to H(2)/H(infinity) control problem for singularly perturbed systems, INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 14(8), 697-717, 20040525
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  168. Approach regions for modified Poisson integrals of boundary functions in Orlicz classes, Far East J. Math. Sci., 14, 137-153, 20040801
  169. Continuity of Sobolev functions of variable exponent on metric spaces, Proc.Japan Acad.Ser.A, 80(6), 96-99, 20040601
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  171. Minimally fine limits at infinity for p-precise functions, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 56(1), 1-15, 200401
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  172. Asymptotic Expansions of Solutions of Cross-coupled Algebraic Riccati Equations of Multimodeling Systems Related to Nash Games, Proceedings of the 3rd International DCDIS Conference on Engineering Applications and Computational Algorithms, 34-39, 20030501
  173. Growth properties for modified Poisson integrals in a half space, Pacific J. Math., 212, 333-346, 20031201
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  175. Growth properties for modified Poisson integrals in a half space, PACIFIC JOURNAL OF MATHEMATICS, 212(2), 333-346, 200312
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  176. Asymptotic expansions and a new numerical algorithm of the algebraic Riccati equation for multiparameter singularly perturbed systems, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 267(1), 209-234, 20020301
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  178. Numerical Algorithm for Solving Cross-Coupled Algebraic Riccati Equations Related to Nash Games of Multimodeling Systems, Proceedings of the 41th IEEE Conference on Decision and Control (CDC), 4167-4172, 20021201
  179. Lindel\"{o}f type theorems for monotone Sobolev functions on half spaces, 1293, 18-26, 20021101
  180. Riesz decomposition and limits at infinity for $p$-precise on a half space, 1293, 98-109, 20021101
  181. Growth properties for modified Poisson integrals in a half space, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 110-123, 20021201
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  183. Growth properties of hyperplane integrals of Sobolev functions in a half space, Osaka J. Math., 38, 759-773, 20011201
  184. Minimally fine limits at infinity for $p$-precice functions, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 61-77, 20011001
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  186. Monotone BLD functions and fine properties, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 50-66, 20000401
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  188. Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball, Ann. Acad. Sci. Fenn. Math., 24, 45-60, 19990401
  189. Exponential integrability for Riesz potentials of functions in Orlicz classes, Hiroshima Math. J., 28, 19980401
  190. Continuity properties and exponential integrability for Riesz potentials of functions in Orlicz classes, 1016, 94-111, 19970401
  191. H\"{o}lder continuity of Riesz potentials of functions in Orlicz classes, 161-172, 19960401
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  193. Integrability of maximal functions for generalized Lebesgue spaces $L^{p(\cdot)}(\log L)^{q(\cdot)}$, Proceedings of the Conference on Potential Theory and Stochastics in Albac: Aurel Cornea Memorial Volume, 193-202, 2009

Invited Lecture, Oral Presentation, Poster Presentation

  1. Boundary behavior of monotone Sobolev functions on John domains, 2017/10/07, With Invitation, Japanese
  2. Sobolev inequalities for Musielak-Orlicz spaces, 下村哲, Nonstandard growth phenomena 2017, 2017/08/31, Without Invitation, Japanese
  3. Sobolev inequalities for variable exponent Orlicz spaces, 2010/08/02, With Invitation, Japanese

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI, 2015, 2017
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  2. KAKENHI, 2012, 2014
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  3. KAKENHI, Study on the problem posing activity in the mathematics education, 2009, 2011
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  4. KAKENHI, Potential theoretic study of elliptic partial differential equations, 2009, 2011
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  5. KAKENHI, Research on potential problems from various aspects, 2008, 2012
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  6. KAKENHI, Potential theoretical research for nonlinear partial differential equations, 2008, 2011
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  7. KAKENHI, Potential theoretic study of Sobolev functions, 2007, 2008
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  8. KAKENHI, Study on the design of broadening mathematical thinking in the mathematics education, 2006, 2008
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  9. KAKENHI, Analyses of function spaces of solutions of a parabolic equation and operators on these spaces, 2006, 2008
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  10. KAKENHI, 2005, 2007
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  11. KAKENHI, New development of geometric function theory focused on conformal invariants, 2005, 2008
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  12. KAKENHI, 2004, 2005
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  13. KAKENHI, Potential Analysis for Sobolev functions, 2002, 2005
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  14. KAKENHI, Study of integral operators on function spaces., 2002, 2003
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  15. KAKENHI, Potential the Oretic study on quasi-regular mappings, 1998, 1999
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  16. KAKENHI(Grant-in-Aid for Scientific Research (C)), 2018, 2020

Social Activities

Organizing Academic Conferences, etc.

  1. Nonstandard growth phenomena 2017, 2017/, 2017/
  2. 調和解析とポテンシャル論, 2015/, 2015/
  3. The 19th International Conference on Finite or Infinite Dimensional complex Analysis and Applications, 2011/
  4. International Workshop on Potential Theory in Hokkaido 2009, 2009/, 2009/
  5. FSDONA (Function Spaces, Differential Operators and Nonlinear Analysis)-Workshop, 2008/, 2008/
  6. 2007/, 2007/