Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Bo‘az Klartag,Emanuel Milman Book 2014 Springer International Publishing Swi

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Vitushkin-Type Theorems,It is shown that for a subset . that has the global Gabrielov property, a Vitushkin-type estimate holds. Concrete examples are given for sub-level sets of certain classes of functions.

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Reflectionless Measures and the Mattila-Melnikov-Verdera Uniform Rectifiability Theorem,The aim of these notes is to provide a new proof of the Mattila-Melnikov-Verdera theorem on the uniform rectifiability of an Ahlfors-David regular measure whose associated Cauchy transform operator is bounded. They are based on lectures given by the second author in the analysis seminars at Kent State University and Tel-Aviv University.

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Estimates for Measures of Sections of Convex Bodies,A . estimate in the hyperplane problem with arbitrary measures has recently been proved in [.]. In this note we present analogs of this result for sections of lower dimensions and in the complex case. We deduce these inequalities from stability in comparison problems for different generalizations of intersection bodies.

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Modified Paouris Inequality,The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of ..-norms and suprema of norms of coordinate projections of isotropic log-concave vectors.

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978-3-319-09476-2Springer International Publishing Switzerland 2014

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