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Sublinear operators with rough kernel generated by Calderón–Zygmund operators and their commutators on generalized Morrey spaces

Abstract

The aim of this paper is to establish the boundedness of certain sublinear operators with rough kernel generated by Calderón–Zygmund operators and their commutators on generalized Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. The Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.

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Correspondence to F. Gürbüz.

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Gürbüz, F. Sublinear operators with rough kernel generated by Calderón–Zygmund operators and their commutators on generalized Morrey spaces. Math Notes 101, 429–442 (2017). https://doi.org/10.1134/S0001434617030051

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Keywords

  • sublinear operator
  • Calderón–Zygmund operator
  • rough kernel
  • generalized Morrey space
  • commutator
  • BMO