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Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces

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Abstract

Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev’s inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger’s inequality and the continuity for Riesz potentials.

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Authors and Affiliations

  1. Faculty of Education and Welfare Science, 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. Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. Czech Math J 64, 209–228 (2014). https://doi.org/10.1007/s10587-014-0095-8

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  • DOI: https://doi.org/10.1007/s10587-014-0095-8

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