Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Bo‘az Klartag,Emanuel Milman Book 2020 Springer Nature Switzerland AG 2020 A

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Barter

,On Discrete Hardy–Littlewood Maximal Functions over the Balls in ,: Dimension-Free Estimates,We show that the discrete Hardy–Littlewood maximal functions associated with the Euclidean balls in . with dyadic radii have bounds independent of the dimension on . for . ∈ [2, .].

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Several Results Regarding the (B)-Conjecture,In the first half of this note we construct Gaussian measures on . which do not satisfy a strong version of the (B)-property. In the second half we discuss equivalent functional formulations of the (B)-conjecture.

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On the Ekeland-Hofer-Zehnder Capacity of Difference Body,It is proven that the Ekeland-Hofer-Zehnder capacity of the difference body of a given convex body . satisfies the following inequality . where . is an absolute constant. Up to a multiplicative constant this inequality is sharp.

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978-3-030-36019-1Springer Nature Switzerland AG 2020

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Geometric Aspects of Functional Analysis978-3-030-36020-7Series ISSN 0075-8434 Series E-ISSN 1617-9692

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