Lower estimates of random unconditional constants of Walsh-Paley martingales with values in banach spaces

1992/02/28 by Stefan Geiß, Geiss, Stefan
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9202203

openalex publication_date 1992/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Banach space X we define RUMDn(X) to be the infimum of all c>0 such that (AVEεk =± 1 || ∑1n epsilonk (Mk - Mk-1 )||L2X2 )1/2 <= c || Mn ||L2X holds for all Walsh-Paley martingales Mk0n subset L2X with M0 =0. We relate the asymptotic behaviour of the sequence RUMD(X)n=1infinity to geometrical properties of the Banach space X such as K-convexity and superreflexivity.

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