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2 results

Trudinger’s inequalities for Riesz potentials in Morrey spaces of double phase functionals on half spaces
Part of
Yoshihiro Mizuta, Tetsu Shimomura
Journal:

Canadian Mathematical Bulletin / Volume 65 / Issue 4 / December 2022

Published online by Cambridge University Press:

27 December 2021, pp. 924-935

Print publication:

December 2022
- Article
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Our aim in this paper is to establish Trudinger’s exponential integrability for Riesz potentials in weighted Morrey spaces on the half space. As an application, we obtain Trudinger’s inequality for Riesz potentials in the framework of double phase functionals.

Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces
Part of
- Linear function spaces and their duals
Takao Ohno, Tetsu Shimomura
Journal:

Canadian Mathematical Bulletin / Volume 63 / Issue 2 / June 2020

Published online by Cambridge University Press:

06 September 2019, pp. 287-303

Print publication:

June 2020
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Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials $I_{\unicode[STIX]{x1D6FC}(\,\cdot \,),\unicode[STIX]{x1D70F}}f$ of order $\unicode[STIX]{x1D6FC}(\,\cdot \,)$ with $f\in L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705},\unicode[STIX]{x1D703}}(X)$ over bounded non-doubling metric measure spaces. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.