Abstract:

Some vector-valued weak Orlicz martingale spaces and three type weak atomics are defined, and the primary theorems of weak atomic decompositions for these weak spaces are established. As an application, the embedding relationships among these martingale spaces are discussed, and the results obtained here are closely connected with the geometric properties of the Banach space.

Key words: Banach space;weak Orlicz martingale spaces;weak atomic decomposion;embedding