Atomic Decompositions for Two-Parameter Vector-Valued Martingales and Two-parameter Vector-valued Martingale Spaces

In this paper atomic decompositions for two-parameter vector-valued martingales are given. With the help of the atomic decompositions the relations between the mutual embedding of two-parameter vector-valued martingale spaces and geometric properties of Banach spaces are investigated. Our study shows that geometric properties of Banach spaces determine the embedding of martingale spaces and conversely the latter can characterize the former. This revised version was published online in June 2006 with corrections to the Cover Date.