B 值复测度拟鞅的原子分解

设P 是一个概率测度,ψ是一个复值可积函数,dμ =ψdP是一个复值测度. 在权函数ψ∈a₁∩b_∝⁺和Banach空间X 具有适当的凸性和光滑性的条件下, 作者证明了关于复测度μ 的X值拟鞅空间D_α(X) 和_pQ_α(X) 上的原子分解定理. 并且利用复测度拟鞅的原子分解定理, 在0<α≤ 1 的情形, 证明了关于X 值复测度拟鞅的两个重要不等式.

Atomic Decompositions of B -valued Quasi-martingales with Respect to Complex Measures

 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.