Inequalities for martingale transforms and related characterizations of Hilbert spaces

Adam Osȩkowski

Statistics & Probability Letters, 2012, vol. 82, issue 1, 186-190

Abstract: 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.

Keywords: Martingale; Martingale transform; Banach space; UMD space; Biconvex function (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.09.021

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