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

Abstract

We consider the commutators [bT] 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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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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Keywords

  • Morrey space
  • Campanato space
  • Variable growth condition
  • Singular integral
  • Fractional integral
  • Commutator

Mathematics Subject Classification

  • 42B35
  • 46E30
  • 42B20
  • 42B25