关键词: 复测度, 向量值拟鞅,  原子分解

Abstract:

 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 D_α(X)  and _pQ_α(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.

Key words: Complex measure,  , Vector-valued quasi-martingale,  , Atomic decomposition