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<p>This paper is devoted to studying the problem of whether the collection of generalized singular integral operators forms an algebra. This kind of problems originates from the famous works of Calderón and Zygmund [Amer. J. Math., 1956], Meyer and Coifman [Cambridge Stud. Adv. Math., 1997]. We demonstrate that all bi-parameter Calderón-Zygmund operators associated to para-accretive functions form an algebra. Our methods are quite different from the orthonormal wavelet bases method used by Meyer and Coifman and discrete Calderón’s reproducing formulas method given by Han, Lee and Lin [J. Fourier. Anal. Appl., 2006]. As a byproduct, a new simple proof was given in the one parameter case.</p>

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The Collection of Calderón-Zygmund Operators Associated to Para-Accretive Functions Forms an Algebra

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Fanghui Liao,
  • Zhengyang Li,
  • Qingying Xue

摘要

This paper is devoted to studying the problem of whether the collection of generalized singular integral operators forms an algebra. This kind of problems originates from the famous works of Calderón and Zygmund [Amer. J. Math., 1956], Meyer and Coifman [Cambridge Stud. Adv. Math., 1997]. We demonstrate that all bi-parameter Calderón-Zygmund operators associated to para-accretive functions form an algebra. Our methods are quite different from the orthonormal wavelet bases method used by Meyer and Coifman and discrete Calderón’s reproducing formulas method given by Han, Lee and Lin [J. Fourier. Anal. Appl., 2006]. As a byproduct, a new simple proof was given in the one parameter case.