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<p>We introduce a bilinear extension of the so-called exotic Calderón-Zygmund operators. These kernels arise naturally from the bilinear singular integrals associated with Zygmund dilations. We show that such a class of operators satisfy a <i>T</i>1 theorem in the same form as the standard Calderón-Zygmund operators. However, one-parameter weighted estimates may fail in general, and unlike the linear case, we are not able to provide the end-point estimates in full generality.</p>

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Bilinear Exotic Calderón-Zygmund Operators

  • 期刊论文

  • 发表日期：

    2025年1月15日

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  • Jin Bai,
  • Jinsong Li,
  • Kangwei Li

摘要

We introduce a bilinear extension of the so-called exotic Calderón-Zygmund operators. These kernels arise naturally from the bilinear singular integrals associated with Zygmund dilations. We show that such a class of operators satisfy a T1 theorem in the same form as the standard Calderón-Zygmund operators. However, one-parameter weighted estimates may fail in general, and unlike the linear case, we are not able to provide the end-point estimates in full generality.