This is an announcement for the paper "Vector-valued decoupling and the Burkholder-Davis-Gundy inequality" by Sonja Cox and Mark Veraar.
Abstract: 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 L^1. 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.
Archive classification: math.FA
Remarks: To appear in the Illinois Journal of Mathematics
Submitted from: sonja.cox@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.2218
or