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

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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 languageEnglish
Pages (from-to)393-426
JournalProceedings of the London Mathematical Society
Volume98
DOIs
Publication statusPublished - 1 Mar 2009

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