L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels

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Abstract

Let μ be a Radon measure on C without atoms. In this paper we prove that if the Cauchy transform is bounded in L2(μ), then all 1-dimensional Calderón-Zygmund operators associated to odd and sufficiently smooth kernels are also bounded in L2(μ).
Original languageEnglish
Pages (from-to)445-479
JournalPublicacions Matematiques
Volume48
DOIs
Publication statusPublished - 1 Jan 2004

Keywords

  • Calderón-zygmund operators
  • Cauchy transform
  • Corona decomposition
  • L estimates 2
  • Non doubling measures

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