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Maximal and Riesz Potential Operators on Musielak–Orlicz Spaces Over Metric Measure Spaces

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Abstract

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator \(M_{\lambda }\) on Musielak–Orlicz spaces \(L^{\Phi }(X)\) over bounded metric measure spaces. As an application of the boundedness of \(M_{\lambda }\), we establish a generalization of Sobolev’s inequality for Riesz potentials \(I_{\alpha (\cdot ),\tau }f\) with \(f \in L^{\Phi }(X)\).

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Acknowledgements

We would like to express our thanks to the referees for their kind comments and helpful suggestions.

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Authors and Affiliations

  1. Faculty of Education, Oita University, Dannoharu, Oita-City, 870-1192, Japan

    Takao Ohno

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

    Tetsu Shimomura

Authors
  1. Takao Ohno
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  2. Tetsu Shimomura
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Correspondence to Takao Ohno.

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Ohno, T., Shimomura, T. Maximal and Riesz Potential Operators on Musielak–Orlicz Spaces Over Metric Measure Spaces. Integr. Equ. Oper. Theory 90, 62 (2018). https://doi.org/10.1007/s00020-018-2484-0

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  • DOI: https://doi.org/10.1007/s00020-018-2484-0

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