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Compactness of Commutators of Integral Operators with Functions in Campanato Spaces on Orlicz-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 the closure of \(C^{\infty }_{\mathrm {comp}}(\mathbb {R}^n)\) with respect to generalized Campanato spaces. We give a necessary and sufficient condition for the compactness of [b, T] and \([b,I_{\rho }]\) on Orlicz-Morrey spaces. The Orlicz-Morrey spaces unify Orlicz and Morrey spaces, and the Campanato spaces unify \(\mathrm {BMO}\) and Lipschitz spaces. Therefore, our results contain many previous results as corollaries.

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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 (C), No. 21K03304, Japan Society for the Promotion of Science.

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

    Satoshi Yamaguchi & Eiichi Nakai

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  1. Satoshi Yamaguchi
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  2. Eiichi Nakai
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Correspondence to Eiichi Nakai.

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Communicated by Karapetyants Alexey.

Dedicated to the 80th anniversary of Professor Stefan Samko.

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Yamaguchi, S., Nakai, E. Compactness of Commutators of Integral Operators with Functions in Campanato Spaces on Orlicz-Morrey Spaces. J Fourier Anal Appl 28, 33 (2022). https://doi.org/10.1007/s00041-022-09920-y

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