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Trudinger-type inequalities in Musielak–Orlicz spaces and double phase functionals

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  27 March 2025

Takao Ohno Open the ORCID record for Takao Ohno [Opens in a new window]  and
Tetsu Shimomura Open the ORCID record for Tetsu Shimomura [Opens in a new window]
Takao Ohno*
Affiliation:
Faculty of Education, Oita University, Dannoharu Oita-city, 870-1192, Japan
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
*
e-mail: t-ohno@oita-u.ac.jp
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Abstract

We establish Trudinger-type inequalities for variable Riesz potentials $J_{\alpha (\cdot ), \tau }f$ of functions in Musielak–Orlicz spaces $L^{\Phi }(X)$ over bounded metric measure spaces X equipped with lower Ahlfors $Q(x)$-regular measures under conditions on $\Phi $ which are weaker than conditions in the previous paper (Houston J. Math. 48 (2022), no. 3, 479–497). We also deal with the case $\Phi $ is the double phase functional with variable exponents. As an application, Trudinger-type inequalities are discussed for Sobolev functions.

Keywords

Riesz potentialsMusielak–Orlicz spacesTrudinger’s inequalitymetric measure spacedouble phase functional

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Secondary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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