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

Details Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality

2008-05-07

arxiv.org/abs/0805.1053v1

Mathematics

Classical Analysis and ODEs

34 pages

Scientific paper

In this paper we study some questions in connection with uniform rectifiability and the $L^2$ boundedness of Calderon-Zygmund operators. We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients which are related to the Jones' $\beta$ numbers. We also use these new coefficients to prove that n-dimensional Calderon-Zygmund operators with odd kernel of type $C^2$ are bounded in $L^2(\mu)$ if $\mu$ is an n-dimensional uniformly rectifiable measure.

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