弱型空间的鞅不等式及其应用

The Martingale Inequalities in Weak-type Spaces and Their Applications

弱型空间是近年来调和分析与鞅论中倍受关注的研究方向,该文就以下几方面介绍有关弱型鞅空间的研究工作:(1)Lorentz鞅空间的原子分解;(2)Orlicz鞅空间的强弱型加权不等式;(3)弱Orlicz鞅空间与拟范数不等式;(4)在Banach空间理论与二进域调和分析中的应用.

In recent years, the weak-type spaces have received more and more attention in Harmonic analysis and Martingale theory. In the paper, we intend to clarify some our study results in weak-type martingale spaces. It consists of four aspects： （1） The atomic decomposition of Lourentz martingale spaces; （2） The strong-type and weak-type weighted inequality for Orlicz martingales; （3） The weak-Orliez martingale spaces and their quasi-normed inequalities; （4） Some applications in Banaeh space theory and the dyadic harmonic analysis.