This is an announcement for the paper “Pointwise properties of martingales with values in Banach function spaces” by Mark Veraarhttps://arxiv.org/find/math/1/au:+Veraar_M/0/1/0/all/0/1, Ivan Yaroslavtsevhttps://arxiv.org/find/math/1/au:+Yaroslavtsev_I/0/1/0/all/0/1.

Abstract: In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new Burkholder--Davis--Gundy type inequality is obtained.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1803.11063