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Trudinger’s Inequality on Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces

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Abstract

We give a generalized Trudinger’s inequality for Riesz potentials \(I_{\alpha (\cdot ),\tau }f\) of functions in Musielak–Orlicz–Morrey spaces \(L^{\Phi ,\kappa ,\theta }(X)\) over bounded non-doubling metric measure spaces X. As a corollary we obtain Trudinger’s inequality for double phase functionals with variable exponents.

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Acknowledgements

The authors would like to thank the referee for giving kind comments and useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, 00014, Helsinki, Finland

    Ritva Hurri-Syrjänen

  2. Faculty of Education, Oita University, Dannoharu Oita-city, 870-1192, Japan

    Takao Ohno

  3. Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima, 739-8524, Japan

    Tetsu Shimomura

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  1. Ritva Hurri-Syrjänen
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  2. Takao Ohno
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  3. Tetsu Shimomura
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Correspondence to Takao Ohno.

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Hurri-Syrjänen, R., Ohno, T. & Shimomura, T. Trudinger’s Inequality on Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces. Mediterr. J. Math. 20, 172 (2023). https://doi.org/10.1007/s00009-023-02383-5

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