TRANSFORMS, DIFFERENTIAL SUBORDINATIONS AND A_p-WEIGHTED INEQUALITIES FOR BANACH-SPACE-VALUED REGULAR MARTINGALES

In this paper we proved the A_p-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A_p-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.