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

Stefan Geiss
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Abstract

For a Banach space X we define RUMD_n(X) to be the infimum of all c>0 such that (AVE_{ε_k =\pm 1} || \sum_1^n epsilon_k (M_k - M_{k-1} )||_{L_2^X}^2 )^{1/2} <= c || M_n ||_{L_2^X} holds for all Walsh-Paley martingales {M_k}_0^n subset L_2^X with M_0 =0. We relate the asymptotic behaviour of the sequence {RUMD(X)}_{n=1}^{infinity} to geometrical properties of the Banach space X such as K-convexity and superreflexivity.

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Stefan Geiss. 1992-02-28. Lower estimates of random unconditional constants of Walsh-Paley martingales with values in banach spaces. https://arxiv.org/abs/math/9202203

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