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Full Description
Volume 245, number 1158 (third of 6 numbers), January 2017.
Contents
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.
