Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality

Xavier Tolsa

doi:https://doi.org/10.1112/plms/pdn035

Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality

Xavier Tolsa

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

38 Citations (Scopus)

Abstract

In this paper we study some questions in connection with uniform rectifiability and the L2 boundedness of Calderón-Zygmund operators (CZOs). We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients that are related to the Jones' β numbers. We also use these new coefficients to prove that n-dimensional CZOs with odd kernel of type script C sign2 are bounded in L 2(μ), if μ is an n-dimensional uniformly rectifiable measure. © 2008 London Mathematical Society.

Original language	English
Pages (from-to)	393-426
Journal	Proceedings of the London Mathematical Society
Volume	98
DOIs	https://doi.org/10.1112/plms/pdn035
Publication status	Published - 1 Mar 2009

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title = "Uniform rectifiability, Calder{\'o}n-Zygmund operators with odd kernel, and quasiorthogonality",

abstract = "In this paper we study some questions in connection with uniform rectifiability and the L2 boundedness of Calder{\'o}n-Zygmund operators (CZOs). We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients that are related to the Jones' β numbers. We also use these new coefficients to prove that n-dimensional CZOs with odd kernel of type script C sign2 are bounded in L 2(μ), if μ is an n-dimensional uniformly rectifiable measure. {\textcopyright} 2008 London Mathematical Society.",

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doi = "https://doi.org/10.1112/plms/pdn035",

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AB - In this paper we study some questions in connection with uniform rectifiability and the L2 boundedness of Calderón-Zygmund operators (CZOs). We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients that are related to the Jones' β numbers. We also use these new coefficients to prove that n-dimensional CZOs with odd kernel of type script C sign2 are bounded in L 2(μ), if μ is an n-dimensional uniformly rectifiable measure. © 2008 London Mathematical Society.

U2 - https://doi.org/10.1112/plms/pdn035

DO - https://doi.org/10.1112/plms/pdn035

M3 - Article

VL - 98

SP - 393

EP - 426

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

ER -