Annals of Functional Analysis

Best possible bounds of the von Bahr--Esseen type

Iosif Pinelis

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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.

Article information

Ann. Funct. Anal., Volume 6, Number 4 (2015), 1-29.

First available in Project Euclid: 1 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 46B09: Probabilistic methods in Banach space theory [See also 60Bxx] 46B20: Geometry and structure of normed linear spaces 46B10: Duality and reflexivity [See also 46A25]

probability inequality concentration of measure product space $p$-uniformly smooth normed space $q$-uniformly convex normed space


Pinelis, Iosif. Best possible bounds of the von Bahr--Esseen type. Ann. Funct. Anal. 6 (2015), no. 4, 1--29. doi:10.15352/afa/06-4-1.

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