Inequalities for martingale transforms and related characterizations of Hilbert spaces

Suppose that f is a martingale taking values in a Banach space B and g is its transform by a deterministic sequence of numbers in {−1,1}, such that supn‖gn‖≥1 almost surely. We show that a certain family of Φ-estimates for f holds true if and only B is a Hilbert space.

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Year of publication:	2012
Authors:	Osȩkowski, Adam
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 1, p. 186-190
Publisher:	Elsevier
Subject:	Martingale \| Martingale transform \| Banach space \| UMD space \| Biconvex function

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040077