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Complex interpolation of vanishing Morrey spaces

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Abstract

We describe the first and second complex interpolations of vanishing Morrey spaces, introduced in Almeida and Samko (J Funct Anal 2726:2392–2411, 2017) and Chiarenza and Franciosi (Ann Mat Pura Appl 161(4):285–297, 1992). In addition, we show that the diamond subspace in Hakim et al. (Constr Approx 46:489–563, 2017) and one of the function spaces in [1] are the same. We also give several examples for showing that each of the complex interpolations of these spaces is different.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their comments and remarks. Sawano was supported by Grant-in-Aid for Scientific Research (C) (16K05209), the Japan Society for the Promotion of Science and Peoples’ Friendship University of Russia.

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Authors and Affiliations

  1. Department of Mathematics, Bandung Institute of Technology, Jl. Ganesha 10, Bandung, 40132, Indonesia

    Denny Ivanal Hakim

  2. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi, Tokyo, 192-0397, Japan

    Yoshihiro Sawano

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

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Communicated by Klaus Guerlebeck.

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Hakim, D.I., Sawano, Y. Complex interpolation of vanishing Morrey spaces. Ann. Funct. Anal. 11, 643–661 (2020). https://doi.org/10.1007/s43034-019-00045-w

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  • DOI: https://doi.org/10.1007/s43034-019-00045-w

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