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Revista Matemática Complutense

, Volume 31, Issue 2, pp 287–331 | Cite as

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

  • Ryutaro Arai
  • Eiichi Nakai
Article
  • 184 Downloads

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.

Keywords

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

Mathematics Subject Classification

42B35 46E30 42B20 42B25 

Notes

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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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.Department of MathematicsIbaraki UniversityMitoJapan

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