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Acta Mathematica Scientia

, Volume 39, Issue 4, pp 1149–1162 | Cite as

Quantitative Weighted Bounds for a Class of Singular Integral Operators

  • Wenhua Gao (高文华)
  • Guoen Hu (胡国恩)Email author
Article
  • 11 Downloads

Abstract

In this article, the authors consider the weighted bounds for the singular integral operator defined by
$${T_A}f(x) = {\rm{p}}.{\rm{v}}.\int_{\mathbb{R}^{n}} {{{{\rm{\Omega }}(x - y)} \over {{\rm{|}}x - y{{\rm{|}}^{n + 1}}}}\left( {A(x) - A(y) - \nabla A(y)} \right)f(y){\rm{d}}y} ,$$
where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on ℝn such that ▽A ∈ BMO(ℝn). By sparse domination, the authors obtain some quantitative weighted bounds for Ta when Ω satisfies regularity condition of Lr-Dini type for some r ∈ (1, ∞).

Key words

Singular integral operator sparse domination Ap constant maximal operator 

2010 MR Subject Classification

42B20 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Applied MathematicsBeijing Normal UniversityZhuhaiChina

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