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2015 Best possible bounds of the von Bahr--Esseen type
Iosif Pinelis
Ann. Funct. Anal. 6(4): 1-29 (2015). DOI: 10.15352/afa/06-4-1

Abstract

The well-known von Bahr--Esseen bound on the absolute $p$th moments of martingales with $p\in(1,2]$ is extended to a large class of moment functions, and now with a best possible constant factor (which depends on the moment function). As an application, measure concentration inequalities for separately Lipschitz functions on product spaces are obtained. Relations with $p$-uniformly smooth and $q$-uniformly convex normed spaces are discussed.

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Iosif Pinelis. "Best possible bounds of the von Bahr--Esseen type." Ann. Funct. Anal. 6 (4) 1 - 29, 2015. https://doi.org/10.15352/afa/06-4-1

Information

Published: 2015
First available in Project Euclid: 1 July 2015

zbMATH: 1319.60036
MathSciNet: MR3365979
Digital Object Identifier: 10.15352/afa/06-4-1

Subjects:
Primary: 60E15
Secondary: 46B09, 46B10, 46B20

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.6 • No. 4 • 2015
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