A general contraction principle for vector-valued martingales

We prove a contraction principle for vector-valued martingales of type [formula] where X is a Banach space with elements x1, ‧‧, xn, (Δi)ni=1 ⊂ L1(Q,P) a martingale difference sequence belonging to a certain class, [formula] a sequence of independent and symmetric random variables exponential in a certain sense, and Ai operators mapping each Δi into a non-negative random variable. Moreover, special operators Ai are discussed and an application to Banach spaces of Rademacher type α (1<α ≤ 2) is given.