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Commutators of Calderón–Zygmund and generalized fractional integral operators on generalized Morrey spaces

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Abstract

We consider the commutators [b, T] and \([b,I_{\rho }]\), where T is a Calderón–Zygmund operator, \(I_{\rho }\) is a generalized fractional integral operator and b is a function in generalized Campanato spaces with variable growth condition. We give necessary and sufficient conditions for the boundedness of the commutator on generalized Morrey spaces with variable growth condition.

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Acknowledgements

The authors would like to thank the referees for their careful reading and many useful comments. The second author was supported by Grant-in-Aid for Scientific Research (B), No. 15H03621, Japan Society for the Promotion of Science.

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

    Ryutaro Arai & Eiichi Nakai

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  1. Ryutaro Arai
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  2. Eiichi Nakai
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Correspondence to Eiichi Nakai.

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Arai, R., Nakai, E. Commutators of Calderón–Zygmund and generalized fractional integral operators on generalized Morrey spaces. Rev Mat Complut 31, 287–331 (2018). https://doi.org/10.1007/s13163-017-0251-4

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  • DOI: https://doi.org/10.1007/s13163-017-0251-4

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