弱Hardy正规鞅空间与原子分解

Weak Hardy Regular Martingale Spaces and Atomic Decompositions

本文证明了弱Hardy正规鞅空间wHp和wHSp上的原子分解定理.利用鞅的原子分解给出了弱Hardy正规鞅空间上的次线性算子有界的一个充分条件.利用这个条件得到了关于正规鞅的一些弱Lp范数不等式和弱(p,p)型不等式.这些结果是经典Hp鞅论中一些重要结果的弱型对应.

In this paper some atomic decomposition theorems for weak Hardy regular martingale space wHp and wH^sp are proved. Using the atomic decompositions of martingale,a sufficient condition for a sublinear operator defined on weak Hardy spaces to be bounded is given. Using the sufficient condition,we obtain some martingale inequa!ities with respect to the weak Lp- norm and some inequalities of weak （19,19） -type. The results are the weak versiotls of the results in the classical martingale Hp theory.