p-光滑性的简单原子刻划

Characterization of p-smooth by Simple Atomic Decompositions

建立了Banach空间值鞅空间pΣq的简单原子分解定理,利用鞅的简单原子分解给出了取值空间p-光滑性的一种刻划。结果表明:B值鞅空间的简单原子分解与鞅的值空间的几何性质之间有着密切的联系。

In this paper,a simple atomic decomposition for Banach-space-valued martingale space pΣq was established.With the help of simple atomic decompositions of martingales,a characterization of p-smooth Banach space in which the martingales took their values was given.The result shows that there exist close relations between simple atomic decompositions of Banach-space-valued martingales and the geometric properties of the Banach space in which the martingales take their values.