Commutators of Cauchy–Fantappiè Type Integrals on Generalized Morrey Spaces on Complex Ellipsoids

Abstract

Let \(\Omega \) be a domain which belongs to a class of bounded weakly pseudoconvex domains of finite type in \({\mathbb {C}}^n\), let \(d\lambda \) be the Monge–Ampère boundary measure on \(b\Omega \) and \(\varrho \ge 0\) be a non-decreasing function. The aim of this paper is to establish the characterizations of boundedness and compactness for the commutator operators of Cauchy–Fantappiè type integrals with \(L^1(b\Omega ,d\lambda )\) functions on the generalized Morrey spaces \(L^{p}_\varrho (b\Omega ,d\lambda )\), with \(p\in (1, \infty )\).

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Acknowledgements

The authors would like to thank the referee(s) for valuable suggestions and comments that led to the improvement of the paper.

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Correspondence to Xuan Thinh Duong.

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A part of the paper was completed during a scientific stay of the authors at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully appreciated. Xuan Thinh Duong was supported by the Australian Research Council through the Discovery Project 190100970. Ly Kim Ha was funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under Grant Number B2019-18-01.

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Dao, N.A., Duong, X.T. & Ha, L.K. Commutators of Cauchy–Fantappiè Type Integrals on Generalized Morrey Spaces on Complex Ellipsoids. J Geom Anal (2021). https://doi.org/10.1007/s12220-020-00561-5

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Keywords

  • BMO
  • VMO
  • Commutators
  • Singular integral operators
  • Convex domains of finite type

Mathematics Subject Classification

  • 47B40
  • 47B70
  • 32A55
  • 32A26
  • 32A37
  • 32A50