Tetsu Shimomura

Last Updated :2021/04/16

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. 2021, Liberal Arts Education Program1, 1Term, CalculusI
  2. 2021, Undergraduate Education, 1Term, Computer Practice
  3. 2021, Undergraduate Education, 2Term, Computer Practice
  4. 2021, Undergraduate Education, 2Term, Research Methods in Analysis I
  5. 2021, Undergraduate Education, 4Term, Study of Instructional Materials in Analysis
  6. 2021, Undergraduate Education, Second Semester, Graduation Thesis
  7. 2021, Undergraduate Education, First Semester, Study of Instructional Materials in Analysis Education
  8. 2021, Undergraduate Education, Second Semester, Practical Seminar for the Teaching Profession
  9. 2021, Graduate Education (Doctoral Program) , 1Term, Research into Curriculum and Instruction Sciences (Specialization in Mathematics Education)
  10. 2021, Graduate Education (Doctoral Program) , 3Term, Research into Curriculum and Instruction Sciences (Specialization in Mathematics Education)
  11. 2021, Graduate Education (Master's Program) , First Semester, Special Study in Mathematics Education A
  12. 2021, Graduate Education (Master's Program) , Second Semester, Special Study in Mathematics Education A
  13. 2021, Graduate Education (Master's Program) , 3Term, Basic Course in Teaching Material Design for Science and Culture (Mathematics) b
  14. 2021, Graduate Education (Doctoral Program) , First Semester, Special Study
  15. 2021, Graduate Education (Doctoral Program) , Second Semester, Special Study

Research Activities

Academic Papers

  1. BOUNDEDNESS OF MAXIMAL OPERATORS ON HERZ SPACES WITH RADIAL VARIABLE EXPONENT, TOHOKU MATHEMATICAL JOURNAL, 72(3), 335-348, 2020
  2. BOUNDARY LIMITS OF MONOTONE SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS, OSAKA JOURNAL OF MATHEMATICS, 57(4), 819-826, 202010
  3. 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
  4. Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces, GEORGIAN MATHEMATICAL JOURNAL, 27(3), 433-439, 202009
  5. Boundedness of the maximal and potential operators in Herz-Morrey type spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 65(9), 1575-1589, 20200901
  6. Growth properties for generalized Riesz potentials of functions satisfying Orlicz conditions, MATHEMATISCHE NACHRICHTEN, 293(6), 1156-1173, 202006
  7. 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
  8. Hardy and Sobolev inequalities in the half space, ACTA MATHEMATICA HUNGARICA, 161(1), 230-244, 202006
  9. Campanato-Morrey spaces for the double phase functionals with variable exponents, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 197, 202008
  10. 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
  11. ★, 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
  12. SOBOLEV'S THEOREM FOR DOUBLE PHASE FUNCTIONALS, MATHEMATICAL INEQUALITIES & APPLICATIONS, 23(1), 17-33, 202001
  13. BOUNDARY GROWTH OF SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 45, 279-292, 2020
  14. 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
  15. 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
  16. 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
  17. OPTIMAL ESTIMATES FOR THE FRACTIONAL HARDY OPERATOR ON VARIABLE EXPONENT LEBESGUE SPACES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 22(2), 445-462, 201904
  18. Lindelof theorems for monotone Sobolev functions in Orlicz spaces on uniform domains, MATHEMATISCHE NACHRICHTEN, 292(4), 793-804, 201904
  19. Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L-1 Over Metric Measure Spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 69(1), 207-223, 201903
  20. BOUNDARY GROWTH OF GENERALIZED RIESZ POTENTIALS ON THE UNIT BALL IN THE VARIABLE SETTINGS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 44, 125-140, 2019
  21. OBSTACLE PROBLEM FOR MUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES, TOHOKU MATHEMATICAL JOURNAL, 71(1), 53-68, 2019
  22. Sobolev's inequality for double phase functionals with variable exponents, FORUM MATHEMATICUM, 31(2), 517-527, 201903
  23. Duality of central Herz-Morrey-Musielak-Orlicz spaces of variable exponents, COLLECTANEA MATHEMATICA, 70(1), 117-151, 201901
  24. 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
  25. Maximal and Riesz Potential Operators on Musielak-Orlicz Spaces Over Metric Measure Spaces, INTEGRAL EQUATIONS AND OPERATOR THEORY, 90(6), 201812
  26. Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball, COLLECTANEA MATHEMATICA, 69(3), 377-394, 201809
  27. 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
  28. ★, 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
  29. VARIABLE EXPONENT WEIGHTED NORM INEQUALITY FOR GENERALIZED RIESZ POTENTIALS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 43(1), 563-577, 2018
  30. GROWTH PROPERTIES OF POTENTIALS IN CENTRAL MORREY-ORLICZ SPACES ON THE UNIT BALL, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 43(1), 21-46, 2018
  31. A remark on modified Morrey spaces on metric measure spaces, HOKKAIDO MATHEMATICAL JOURNAL, 47(1), 1-15, 201802
  32. SOBOLEV'S INEQUALITIES FOR HERZ-MORREY-ORLICZ SPACES ON THE HALF SPACE, MATHEMATICAL INEQUALITIES & APPLICATIONS, 21(2), 433-453, 201804
  33. Sobolev inequalities for Musielak-Orlicz spaces, MANUSCRIPTA MATHEMATICA, 155(1-2), 209-227, 201801
  34. Growth properties for Riesz potentials of functions in weighted variable Lp(.) spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 162, 49-75, 201710
  35. BOUNDEDNESS OF THE MAXIMAL OPERATOR ON MUSIELAK-ORLICZ-MORREY SPACES, TOHOKU MATHEMATICAL JOURNAL, 69(4), 483-495, 2017
  36. Duality of Non-Homogeneous Central Herz-Morrey-Musielak-Orlicz Spaces, POTENTIAL ANALYSIS, 47(4), 447-460, 2017
  37. 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
  38. 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
  39. 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
  40. Generalized fractional integral operators over non-doubling metric measure spaces, INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 28(7), 534-546, 201707
  41. Growth properties near the origin for generalized Riesz potentials, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 454(1), 285-302, 2017
  42. SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN Lp(.) OVER NONDOUBLING MEASURE SPACES, BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 93(1), 128-136, 2016
  43. 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
  44. SOME NORM INEQUALITIES IN MUSIELAK-ORLICZ SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 41(2), 721-744, 2016
  45. Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 66(2), 371-394, 2016
  46. 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
  47. 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
  48. Growth properties of Musielak-Orlicz integral means for Riesz potentials, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 112, 69-83, 201501
  49. Boundary limits of monotone Sobolev functions with variable exponent on uniform domains in a metric space, REVISTA MATEMATICA COMPLUTENSE, 28(1), 31-48, 201501
  50. SOBOLEV AND TRUDINGER TYPE INEQUALITIES ON GRAND MUSIELAK-ORLICZ-MORREY SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 40(1), 403-426, 2015
  51. Musielak-Orlicz-Sobolev spaces on metric measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 65(2), 435-474, 201506
  52. Weighted Morrey spaces of variable exponent and Riesz potentials, MATHEMATISCHE NACHRICHTEN, 288(8-9), 984-1002, 201506
  53. 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
  54. Problem posing in the upper grades using computers, Mathematical Problem Posing, Springer-Verlag New York, 257-272, 2015
  55. Optimal estimates for the fractional Hardyoperator, STUDIA MATHEMATICA, 227(1), 1-19, 2015
  56. 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
  57. Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces, BULLETIN DES SCIENCES MATHEMATIQUES, 138(2), 225-235, 201403
  58. 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
  59. 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
  60. 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
  61. Hardy's inequality in Musielak-Orlicz-Sobolev spaces, HIROSHIMA MATHEMATICAL JOURNAL, 44(2), 139-155, 201407
  62. 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
  63. Trudinger's Inequality and Continuity of Potentials on Musielak-Orlicz-Morrey Spaces, POTENTIAL ANALYSIS, 38(2), 515-535, 201302
  64. ★, Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces, BULLETIN DES SCIENCES MATHEMATIQUES, 137(1), 76-96, 2013
  65. On the Boundary Limits of Monotone Sobolev Functions in Variable Exponent Orlicz Spaces, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 29(3), 461-470, 201303
  66. 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
  67. 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
  68. Hardy Averaging Operator on Generalized Banach Function Spaces and Duality, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 32(2), 233-255, 2013
  69. Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents, COLLECTANEA MATHEMATICA, 64(3), 313-350, 201309
  70. Approximate identities and Young type inequalities in Musielak-Orlicz spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 63(4), 933-948, 201312
  71. 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
  72. Mean continuity for potentials of functions in Musielak-Orlicz spaces, RIMS K\^{o}ky\^{u}roku Bessatsu., B43, 81-100, 20130901
  73. Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces, JOURNAL OF INEQUALITIES AND APPLICATIONS, 1-19, 2013
  74. LINDELOF THEOREMS FOR MONOTONE SOBOLEV FUNCTIONS IN ORLICZ SPACES, ILLINOIS JOURNAL OF MATHEMATICS, 57(4), 1025-1033, 2013
  75. Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in R-n, REVISTA MATEMATICA COMPLUTENSE, 25(2), 413-434, 201207
  76. A trace inequality of Riesz potentials in variable exponent Orlicz spaces, MATHEMATISCHE NACHRICHTEN, 285(11-12), 1466-1485, 201208
  77. Weighted Sobolev inequality in Musielak-Orlicz space, J. Math. Anal. Appl., 388, 86-97, 20120101
  78. Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Orlicz-Musielak spaces, Arch. Math., 98, 253-263, 20120301
  79. Weighted Sobolev inequality in Musielak-Orlicz space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 388(1), 86-97, 20120401
  80. Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces, ARCHIV DER MATHEMATIK, 98(3), 253-263, 201203
  81. EXPONENTIAL INTEGRABILITY OF RIESZ POTENTIALS OF ORLICZ FUNCTIONS, ILLINOIS JOURNAL OF MATHEMATICS, 56(2), 507-520, 2012
  82. Iterated maximal functions in variable exponent Lebesgue spaces, MANUSCRIPTA MATHEMATICA, 135(3-4), 381-399, 201107
  83. Capacity for potentials of functions in Musielak-Orlicz spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 74(17), 6231-6243, 201112
  84. Hardy's inequality in Orlicz-Sobolev spaces of variable exponent, HOKKAIDO MATHEMATICAL JOURNAL, 40(2), 187-203, 201106
  85. Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 56(7-9), 671-695, 2011
  86. ORLICZ-SOBOLEV CAPACITY OF BALLS, ILLINOIS JOURNAL OF MATHEMATICS, 55(2), 543-553, 2011
  87. 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
  88. Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent, BULLETIN DES SCIENCES MATHEMATIQUES, 134(1), 12-36, 2010
  89. Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 366(2), 391-417, 20100615
  90. 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
  91. SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS, GLASGOW MATHEMATICAL JOURNAL, 52, 227-240, 201005
  92. 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
  93. Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form, MATHEMATISCHE NACHRICHTEN, 283(9), 1336-1352, 201009
  94. CONTINUITY PROPERTIES FOR RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES OF VARIABLE EXPONENT, MATHEMATICAL INEQUALITIES & APPLICATIONS, 13(1), 99-122, 201001
  95. WEIGHTED ORLICZ-RIESZ CAPACITY OF BALLS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138(12), 4291-4302, 201012
  96. Variable exponent spaces on metric measure spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr and Nicolosi (ed.)), 107-121, 2009
  97. Continuity properties of Riesz potentials of Orlicz functions, Tohoku Mathematical Journal, 61(2), 225-240, 20090601
  98. CONTINUITY PROPERTIES OF RIESZ POTENTIALS OF ORLICZ FUNCTIONS, TOHOKU MATHEMATICAL JOURNAL, 61(2), 225-240, 200906
  99. SOBOLEV'S INEQUALITY FOR RIESZ POTENTIALS OF FUNCTIONS IN NON-DOUBLING MORREY SPACES, OSAKA JOURNAL OF MATHEMATICS, 46(1), 255-271, 200903
  100. ★, MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 34(2), 503-522, 2009
  101. 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
  102. Integrability of maximal functions in Orlicz spaces of variable exponent, 京都大学数理解析研究所講究録, 1669, 37-51, 2009
  103. 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
  104. 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
  105. Lindel\"of theorems for monotone Sobolev functions with variable exponent, Proc. Japan Acad. Ser. A Math. Sci., 84, 25-28, 20080201
  106. 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
  107. Lindelof theorems for monotone Sobolev functions with variable exponent, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 84(2), 25-28, 200802
  108. Integrability of maximal functions for generalized Lebesgue spaces with variable exponent, MATHEMATISCHE NACHRICHTEN, 281(3), 386-395, 2008
  109. 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
  110. Continuity properties and vanishing exponential integrability of Riesz potentials of Orlicz functions, 1553, 137-148, 2007
  111. Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes, ILLINOIS JOURNAL OF MATHEMATICS, 51(4), 1039-1060, 2007
  112. Sobolev embeddings for Riesz potential space of variable exponent on metric spaces, Ann. Acad. Sci. Fenn. Math., 31, 495-522, 20060601
  113. Sobolev embeddings for Riesz potential space of variable exponent, Math. Nachr., 279, 1463-1473, 20060401
  114. Sobolev embeddings for variable exponent Riesz potentials on metric spaces {\bf 31} (2006),, Ann. Acad. Sci. Fenn. Math., 31, 495-522, 20060401
  115. Sobolev embedding theorems for variable exponent Riesz potentials, 22, 21-30, 20060401
  116. 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
  117. Approach regions for modified Poisson integrals of boundary functions in Orlicz classes, Far East J. Math. Sci., 14, 137-153, 20040801
  118. Continuity of Sobolev functions of variable exponent on metric spaces, Proc.Japan Acad.Ser.A, 80(6), 96-99, 20040601
  119. Sobolev embeddings for Riesz potential space of variable exponent, 109-115, 20040801
  120. Minimally fine limits at infinity for p-precise functions, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 56(1), 1-15, 200401
  121. 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
  122. Growth properties for modified Poisson integrals in a half space, Pacific J. Math., 212, 333-346, 20031201
  123. On semi-fine limits at infinity for Riesz potentials and monotone BLD functions, POTENTIAL ANALYSIS, 19(4), 365-381, 200312
  124. Growth properties for modified Poisson integrals in a half space, PACIFIC JOURNAL OF MATHEMATICS, 212(2), 333-346, 200312
  125. 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
  126. Near-Optimal Control of Linear Multiparameter Singularly Perturbed Systems, IEEE Transactions on Automatic Control, 47(12), 2051-2057, 20021201
  127. 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
  128. Lindel\"{o}f type theorems for monotone Sobolev functions on half spaces, 1293, 18-26, 20021101
  129. Riesz decomposition and limits at infinity for $p$-precise on a half space, 1293, 98-109, 20021101
  130. Growth properties for modified Poisson integrals in a half space, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 110-123, 20021201
  131. Continuity and differentiability for weighted Sobolev spaces, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 130(10), 2985-2994, 2002
  132. Growth properties of hyperplane integrals of Sobolev functions in a half space, Osaka J. Math., 38, 759-773, 20011201
  133. Minimally fine limits at infinity for $p$-precice functions, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 61-77, 20011001
  134. Growth properties of spherical means for monotone BLD functions in the unit ball, Ann. Acad. Sci. Fenn. Math., 25, 457-465, 20000401
  135. Monotone BLD functions and fine properties, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 50-66, 20000401
  136. Hyperplane integrals of BLD and monotone BLD functions, 1116, 51-68, 19990401
  137. Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball, Ann. Acad. Sci. Fenn. Math., 24, 45-60, 19990401
  138. Exponential integrability for Riesz potentials of functions in Orlicz classes, Hiroshima Math. J., 28, 19980401
  139. Continuity properties and exponential integrability for Riesz potentials of functions in Orlicz classes, 1016, 94-111, 19970401
  140. H\"{o}lder continuity of Riesz potentials of functions in Orlicz classes, 161-172, 19960401
  141. Taylor expansion of Riesz potentials, Hiroshima Math. J., 25, 595-621, 19951101

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

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/