Atomic Decompositions of B -valued Quasi-martingales with Respect to Complex Measures
B 值复测度拟鞅的原子分解

Let P be a probability measure, ψ a complex valued integrable function and dμ=ψdP a complex valued measure. Two theorems of atomic decompositions for the space Dα(X) and pQα(X) of X-valued quasi-martingales with respect to the complex measure μ are obtained when ψ ∈a1 ∩ b∝+ and the Banach space X has suitable convexity and smoothness. As the applications of atomic decompositions two inequalities are proved for X-valued quasi-martingales respect to the complex measures μ by using atomic decompositions in the case of 0< α ≤ 1.