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Let X be a Banach space. We prove p-independence of the one-sided decouplinginequality for X-valued tangent martingales as introduced by Kwapien andWoyczynski. It is known that a Banach space X satisfies the two-sideddecoupling inequality if and only if X is a UMD Banach space. The one-sideddecoupling inequality is a weaker property, including e.g. the space L^1. Weprovide information on the optimal constants for various spaces, and give aupper estimate of order p in general. In the second part of our paper we deriveBurkholder-Davis-Gundy type estimates for p-th moments, p in (0,infty), ofX-valued stochastic integrals, provided X is a UMD Banach space or a space inwhich the one-sided decoupling inequality holds.

Vector-valued decoupling and the Burkholder-Davis-Gundy inequality