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Two Weighted Herz Spaces with Variable Exponents

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Abstract

Our aim is to define the two weighted Herz spaces with variable exponents and develop the theory on the spaces. We first characterize the spaces in terms of the two critical constant exponents. Finally we prove the boundedness of the commutators of singular integrals with BMO functions.

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Acknowledgements

The authors are thankful to reviewers for their careful reading of this paper and their comments. The first author was partially supported by Grand-in-Aid for Scientific Research (C), No. 15K04928, for Japan Society for the Promotion of Science. The second author was partially supported by Grand-in-Aid for Scientific Research (C), No. 16K05212, for Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Faculty of Education, Okayama University, 3-1-1 Tsushima-naka, Okayama, 700-8530, Japan

    Mitsuo Izuki

  2. Department of Mathematics and Information Science, Tokyo Metropolitan University, Hachioji, 192-0397, Japan

    Takahiro Noi

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  1. Mitsuo Izuki
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  2. Takahiro Noi
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Correspondence to Mitsuo Izuki.

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Communicated by Rosihan M. Ali.

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Izuki, M., Noi, T. Two Weighted Herz Spaces with Variable Exponents. Bull. Malays. Math. Sci. Soc. 43, 169–200 (2020). https://doi.org/10.1007/s40840-018-0671-4

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  • DOI: https://doi.org/10.1007/s40840-018-0671-4

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