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Complex interpolation of various subspaces of Morrey spaces

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Abstract

In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces. We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al. (2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano (2017) and Hakim et al. (2017).

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Acknowledgements

The second author was supported by Grant-in-Aid for Scientific Research (C) (Grant No. 16K05209), Japan Society for the Promotion of Science and Department of Mathematics Analysis and the Theory of Functions, Peoples’ Friendship University of Russia. The authors thank the referees for their useful comments.

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Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Tokyo, 192-0397, Japan

    Denny Ivanal Hakim & Yoshihiro Sawano

  2. Department of Mathematics, Bandung Institute of Technology, Bandung, 40132, Indonesia

    Denny Ivanal Hakim

  3. Department of Mathematics Analysis and the Theory of Functions, Peoples’ Friendship University of Russia, Moscow, 117198, Russia

    Yoshihiro Sawano

Authors
  1. Denny Ivanal Hakim
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  2. Yoshihiro Sawano
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Correspondence to Denny Ivanal Hakim.

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Hakim, D.I., Sawano, Y. Complex interpolation of various subspaces of Morrey spaces. Sci. China Math. 63, 937–964 (2020). https://doi.org/10.1007/s11425-017-9318-0

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  • DOI: https://doi.org/10.1007/s11425-017-9318-0

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