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Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent |
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| Authors: | Toshihide Futamura Yoshihiro Mizuta |
| Institution: | a Department of Mathematics, Daido University, Nagoya 457-8530, Japan b Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8521, Japan c Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan |
| Abstract: | Our aim in this paper is to deal with Sobolev's type inequality, Hardy's type inequality and Trudinger's inequality for Riesz potentials of functions in Orlicz spaces of variable exponent. These results are based on the boundedness of maximal operators and so-called Hedberg's trick. Our methods can also be applied to the case of constant exponents with slight modifications. |
| Keywords: | Maximal functions Variable exponent Sobolev's inequality Hardy's inequality Trudinger's inequality Riesz potentials |
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