鞅空间理论的新进展
THE NEW PROGRESS IN MARTINGALE SPACE THEORY

本文是一篇综述性的文字，内容主要是近年来有关鞅空间理论的发展状况，特别是集中于B-值鞅和弱型鞅空间两个部分，可以看做是整个鞅空间理论发展的一个侧面.希望以此引起读者对鞅论的了解和进一步研究的兴趣.具体内容分为以下三节：1.研究鞅空间理论的意义，阐述鞅空间理论与调和分析的关系；2.鞅空间理论的向量值化，阐述B-值鞅不等式与Banach空间几何学的相互依存关系；3.弱型鞅空间与变指数鞅空间的不等式及其应用.
In this paper, we present some new progress in martingale space theory:including vector-valued martingale spaces and weak-type martingale spaces. The paper includes three sections:1. The significance to study martingale space theory, a description for the relation of martingale theory with harmonic analysis; 2. The Banach-space-valued martingales, a expression of the relation of martingale theory with the geometry in Banach spaces; 3. The weak-type martingale spaces and the variable exponent martingale spaces