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Trudinger’s inequalities for Riesz potentials in Morrey spaces of double phase functionals on half spaces

Part of: Linear function spaces and their duals Higher-dimensional theory Harmonic analysis in several variables

Published online by Cambridge University Press:  27 December 2021

Yoshihiro Mizuta  and
Tetsu Shimomura
Yoshihiro Mizuta
Affiliation:
Department of Mathematics, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8521, Japan e-mail: yomizuta@hiroshima-u.ac.jp
Tetsu Shimomura*
Affiliation:
Department of Mathematics, Graduate School of Humanities and Social Sciences, Hiroshima University, Higashi-Hiroshima 739-8524, Japan
*
e-mail: tshimo@hiroshima-u.ac.jp
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Abstract

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.

Keywords

Riesz potentialsSobolev’s inequalityTrudinger’s inequalityweighted Morrey spacedouble phase functional

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 31B15: Potentials and capacities, extremal length

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 4 , December 2022 , pp. 924 - 935
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Copyright
© Canadian Mathematical Society, 2021

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