Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality - Mathematics > Classical Analysis and ODEsReport as inadecuate




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Abstract: In this paper we study some questions in connection with uniformrectifiability and the $L^2$ boundedness of Calderon-Zygmund operators. We showthat uniform rectifiability can be characterized in terms of some newadimensional coefficients which are related to the Jones- $\beta$ numbers. Wealso use these new coefficients to prove that n-dimensional Calderon-Zygmundoperators with odd kernel of type $C^2$ are bounded in $L^2\mu$ if $\mu$ isan n-dimensional uniformly rectifiable measure.



Author: Xavier Tolsa

Source: https://arxiv.org/



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