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Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

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Abstract

The aim of this paper is to give a Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over spaces of homogeneous type.

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Authors and Affiliations

  1. Department of Mechanical Systems Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake Saeki-ku, Hiroshima, 731-5193, Japan

    Yoshihiro Mizuta

  2. Department of Mathematics, Ibaraki University, Mito, Ibaraki, 310-8512, Japan

    Eiichi Nakai

  3. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Yoshihiro Sawano

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

    Tetsu Shimomura

Authors
  1. Yoshihiro Mizuta
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  2. Eiichi Nakai
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  3. Yoshihiro Sawano
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  4. Tetsu Shimomura
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Correspondence to Eiichi Nakai.

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Mizuta, Y., Nakai, E., Sawano, Y. et al. Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces. Arch. Math. 98, 253–263 (2012). https://doi.org/10.1007/s00013-012-0362-6

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  • DOI: https://doi.org/10.1007/s00013-012-0362-6

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