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Weighted Norm Inequalities for Commutators of BMO Functions and Singular Integral Operators with Non-Smooth Kernels

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Abstract

The aim of this paper is to establish a sufficient condition for certain weighted norm inequalities for singular integral operators with non-smooth kernels and for the commutators of these singular integrals with BMO functions. Our condition is applicable to various singular integral operators, such as the second derivatives of Green operators associated with Dirichlet and Neumann problems on convex domains, the spectral multipliers of non-negative self-adjoint operators with Gaussian upper bounds, and the Riesz transforms associated with magnetic Schrödinger operators.

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Acknowledgements

This paper is part of the first-named author’s PhD thesis. The authors would like to thank the referees for useful comments to improve the paper, including a suggestion to correct an argument in the proof of Theorem 3.1. The authors also thank L. Yan for helpful discussion.

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Authors and Affiliations

  1. Department of Mathematics, Macquarie University, North Ryde, NSW, 2109, Australia

    The Anh Bui & Xuan Thinh Duong

  2. Department of Mathematics, University of Pedagogy, Ho Chi Minh City, Vietnam

    The Anh Bui

Authors
  1. The Anh Bui
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  2. Xuan Thinh Duong
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Correspondence to Xuan Thinh Duong.

Additional information

Communicated by Der-Chen Chang.

The Anh Bui was supported by a Macquarie University scholarship.

Xuan Thinh Duong was supported by a research grant from Macquarie University.

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Bui, T.A., Duong, X.T. Weighted Norm Inequalities for Commutators of BMO Functions and Singular Integral Operators with Non-Smooth Kernels. J Geom Anal 24, 1368–1397 (2014). https://doi.org/10.1007/s12220-012-9377-2

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  • DOI: https://doi.org/10.1007/s12220-012-9377-2

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