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<p>This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type (1,&#xa0;1) estimate of noncommutative maximal Calderón-Zygmund operators, corresponding version of square functions and a weighted <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_1- L_1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> type inequality. All these results are obtained under the condition that the weight belonging to the Muchenhoupt <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> class and certain regularity assumptions imposed on kernels which are weaker than the Lipschitz condition.</p>

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Weighted Norm Estimates of Noncommutative Calderón-Zygmund Operators

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Wenfei Fan,
  • Yong Jiao,
  • Lian Wu,
  • Dejian Zhou

摘要

This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type (1, 1) estimate of noncommutative maximal Calderón-Zygmund operators, corresponding version of square functions and a weighted \(H_1- L_1\) H 1 - L 1 type inequality. All these results are obtained under the condition that the weight belonging to the Muchenhoupt \(A_1\) A 1 class and certain regularity assumptions imposed on kernels which are weaker than the Lipschitz condition.