2011/07/12 by Sonja Cox, Mark Veraar, Cox, Sonja +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR
paper · pdf · doi:10.48550/arxiv.1107.2218
To appear in the Illinois Journal of Mathematics
arxiv created 2012/08/26 · arxiv updated 2012/08/28
Let X be a Banach space. We prove p-independence of the one-sided decoupling inequality for X-valued tangent martingales as introduced by Kwapien and Woyczynski. It is known that a Banach space X satisfies the two-sided decoupling inequality if and only if X is a UMD Banach space. The one-sided decoupling inequality is a weaker property, including e.g. the space L1. We provide information on the optimal constants for various spaces, and give a upper estimate of order p in general. In the second part of our paper we derive Burkholder-Davis-Gundy type estimates for p-th moments, p in (0,infty), of X-valued stochastic integrals, provided X is a UMD Banach space or a space in which the one-sided decoupling inequality holds.