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Complex Variables and Elliptic Equations
An International Journal
Volume 56, 2011 - Issue 7-9: Sobolev Spaces with Variable Exponent and Related Elliptic Problems: Theory and Applications; Guest Editors: Alexander Pankov, Robert P. Gilbert, Stanislav Antontsev and Vicentiu Radulescu
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Original Articles

Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

Yoshihiro Mizuta The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan
,
Eiichi Nakai Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
,
Takao Ohno General Arts, Hiroshima National College of Maritime Technology, Higashino Oosakikamijima Toyotagun 725-0231, JapanCorrespondence[email protected]
&
Tetsu Shimomura Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan
Pages 671-695 | Received 13 Nov 2009, Accepted 26 Apr 2010, Published online: 13 Jan 2011

Citations (33)

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Takao Ohno & Tetsu Shimomura. (2022) Sobolev's inequality in central Herz-Morrey-Musielak-Orlicz spaces over metric measure spaces. Complex Variables and Elliptic Equations 67:5, pages 1154-1185.
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Kwok-Pun Ho. (2018) The Ahlfors–Beurling transform on Morrey spaces with variable exponents. Integral Transforms and Special Functions 29:3, pages 207-220.
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Yoshihiro Mizuta & Takao Ohno. (2015) Herz–Morrey spaces of variable exponent, Riesz potential operator and duality. Complex Variables and Elliptic Equations 60:2, pages 211-240.
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Yoshihiro Sawano & Tetsu Shimomura. (2014) Sobolev embeddings for Riesz potentials of functions in Musielak–Orlicz–Morrey spaces over non-doubling measure spaces. Integral Transforms and Special Functions 25:12, pages 976-991.
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Articles from other publishers (29)

Takao Ohno & Tetsu Shimomura. (2023) Continuity of Generalized Riesz Potentials for Double Phase Functionals with Variable Exponents over Metric Measure Spaces. Taiwanese Journal of Mathematics 27:4.
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Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2023) Hardy–Littlewood–Sobolev Theorem for Variable Riesz Potentials. Results in Mathematics 78:3.
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Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2023) Sobolev’s Inequality for Musielak–Orlicz–Sobolev Functions. Results in Mathematics 78:3.
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Ritva Hurri-Syrjänen, Takao Ohno & Tetsu Shimomura. (2023) Trudinger’s Inequality on Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces. Mediterranean Journal of Mathematics 20:3.
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Takao Ohno & Tetsu Shimomura. (2022) Sobolev-Type Inequalities on Musielak–Orlicz–Morrey Spaces of an Integral Form. Bulletin of the Malaysian Mathematical Sciences Society 46:1.
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Takao Ohno & Tetsu Shimomura. (2021) Sobolev-type inequalities on variable exponent Morrey spaces of an integral form. Ricerche di Matematica 71:1, pages 189-204.
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T. Ohno & T. Shimomura. (2022) Generalized fractional integral operators on variable exponent Morrey spaces of an integral form. Acta Mathematica Hungarica 167:1, pages 201-214.
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Takao Ohno & Tetsu Shimomura. (2021) Continuity of generalized Riesz potentials for double phase functionals with variable exponents. Glasnik Matematicki 56:2, pages 329-341.
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Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2021) Boundedness of fractional maximal operators for double phase functionals with variable exponents. Journal of Mathematical Analysis and Applications 501:1, pages 124360.
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Yoshihiro Mizuta & Tetsu Shimomura. (2021) Sobolev type inequalities for fractional maximal functions and Green potentials in half spaces. Positivity 25:3, pages 1131-1146.
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TAKAO OHNO & TETSU SHIMOMURA. (2019) SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES. Journal of the Australian Mathematical Society 110:3, pages 371-385.
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Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2021) Boundedness of maximal operator, Hardy operator and Sobolev’s inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces. Hiroshima Mathematical Journal 51:1.
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Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno & Tetsu Shimomura. (2019) Campanato–Morrey spaces for the double phase functionals. Revista Matemática Complutense 33:3, pages 817-834.
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Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno & Tetsu Shimomura. (2020) Campanato–Morrey spaces for the double phase functionals with variable exponents. Nonlinear Analysis 197, pages 111827.
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Takao Ohno & Tetsu Shimomura. (2019) Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces. Canadian Mathematical Bulletin 63:2, pages 287-303.
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Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2019) Sobolev’s inequality for double phase functionals with variable exponents. Forum Mathematicum 31:2, pages 517-527.
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Takao Ohno & Tetsu Shimomura. (2018) Sobolev's inequality for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces. Mathematische Nachrichten 291:10, pages 1547-1562.
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Takao Ohno & Tetsu Shimomura. (2016) 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.
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Pinhong Long & Huili Han. (2016) Characterizations of some operators on the vanishing generalized Morrey spaces with variable exponent. Journal of Mathematical Analysis and Applications 437:1, pages 419-430.
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Yoshihiro Mizuta & Tetsu Shimomura. (2015) Weighted Morrey spaces of variable exponent and Riesz potentials. Mathematische Nachrichten 288:8-9, pages 984-1002.
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Takao Ohno & Tetsu Shimomura. (2014) 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, pages 1-17.
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Takao Ohno & Tetsu Shimomura. (2014) Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. Czechoslovak Mathematical Journal 64:1, pages 209-228.
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Eiichi Nakai. (2014) Generalized fractional integrals on generalized Morrey spaces. Mathematische Nachrichten 287:2-3, pages 339-351.
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Yoshihiro Sawano & Tetsu Shimomura. (2013) 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 2013:1.
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Yoshihiro Sawano & Tetsu Shimomura. (2013) Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents. Collectanea Mathematica 64:3, pages 313-350.
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Yoshihiro MIZUTA, Eiichi NAKAI, Yoshihiro SAWANO & Tetsu SHIMOMURA. (2013) Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials. Journal of the Mathematical Society of Japan 65:2.
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Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2012) Trudinger’s Inequality and Continuity of Potentials on Musielak–Orlicz–Morrey Spaces. Potential Analysis 38:2, pages 515-535.
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Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno & Tetsu Shimomura. (2013) Boundedness of maximal operators and Sobolevʼs inequality on Musielak–Orlicz–Morrey spaces. Bulletin des Sciences Mathématiques 137:1, pages 76-96.
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Yoshihiro Mizuta & Tetsu Shimomura. (2012) A trace inequality of Riesz potentials in variable exponent Orlicz spaces. Mathematische Nachrichten 285:11-12, pages 1466-1485.
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