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Weighted Morrey spaces of variable exponent and Riesz potentials |
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| Authors: | Yoshihiro Mizuta Tetsu Shimomura |
| Institution: | 1. +81 2. 82 3. 921 4. 5461+81 82 921 8973;5. Department of Mechanical Systems Engineering, Hiroshima Institute of Technology, Saeki‐ku, Hiroshima, Japan;6. Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi‐Hiroshima, Japan |
| Abstract: | We prove weighted inequalities for the Hardy‐Littlewood maximal operator on weighted Morrey spaces  of variable exponent. As an application of the boundedness of the maximal operator, we establish weighted Sobolev's inequality for Riesz potentials. We are also concerned with weighted Trudinger's inequality for Riesz potentials. |
| Keywords: | Maximal function Riesz potentials Sobolev's inequality Trudinger's inequality Morrey spaces of variable exponent weights 31B15 46E30 |