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On Strongly Orthogonal Martingales in Umd Banach Spaces

Yaroslavtsev Ivan S.

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 1

153--171

In the present paper we introduce the notion of strongly orthogonal martingales. Moreover, we show that for any UMD Banach space X and for any X-valued strongly orthogonal martingales M and N such that N is weakly differentially subordinate to M, one has, for all 1 < p < 1, [formula] with the sharp constant χp;X being the norm of a decoupling-type martingale transform and lying in the range, [formula], where βp;X is the UMDp constant of X, hp;X is the norm of the Hilbert transform on Lp(R; X), [formula] are the Gaussian decoupling constants.