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# Rectifiable measures, square functions involving densities, and the cauchy transform

Author: Xavier Tolsa Providence, Rhode Island : American Mathematical Society, 2017. Memoirs of the American Mathematical Society, no. 1158. Print book : EnglishView all editions and formats Volume 245, number 1158 (third of 6 numbers), January 2017. (not yet rated) 0 with reviews - Be the first.

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Document Type: Book Xavier Tolsa Find more information about: Xavier Tolsa 9781470422523 1470422522 960091026 "Volume 245, number 1158 (third of 6 numbers), January 2017." v, 130 pages : illustrations ; 26 cm. Introduction Preliminaries A compactness argument The dyadic lattice of cells with small boundaries The Main Lemma The stopping cells for the proof of Main Lemma 5.1 The measure $\tilde\mu$ and some estimates about its flatness} The measure of the cells from $\mathsf{BCF}$, $\mathsf{LD}$, $\mathsf{BSD}$ and $\mathsf{BCG}$ The new families of cells $\mathsf{BS}\beta$, $\mathsf{NTerm}$, $\mathsf{NGood}$, $\mathsf{NQgood}$ and $\mathsf{NReg}$ The approximating curves $\Gamma^k$ The small measure $\tilde\mu$ of the cells from $\mathsf{BS}\beta$ The approximating measure $\nu^k$ on $\Gamma^k_{ex}$ Square function estimates for $\nu^k$ The good measure $\sigma^k$ on $\Gamma^k$ The $L^2(\sigma^k)$ norm of the density of $\nu^k$ with respect to $\sigma^k$ The end of the proof of the Main Lemma 5.1 Proof of Theorem 1.3: Boundedness of $T_\mu$ implies boundedness of the Cauchy transform Some Calderon-Zygmund theory for $T_\mu$ Proof of Theorem 1.3: Boundedness of the Cauchy transform implies boundedness of $T_\mu$ Bibliography. Memoirs of the American Mathematical Society, no. 1158. Xavier Tolsa.

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