弱型空间的鞅不等式及其应用——纪念李国平院士吴新谋教授诞辰100周年

摘要/Abstract

摘要：

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.

关键词: 鞅论, 原子分解, 加权不等式, 拟赋范空间

Abstract:

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-Orlicz martingale spaces and their quasi-normed inequalities; (4) Some applications in Banach space theory and the dyadic harmonic analysis.

Key words: Martingale theory, Atomic decomposition, Weighted inequality, Quasi-normed space

中图分类号:

60G42

刘培德. 弱型空间的鞅不等式及其应用——纪念李国平院士吴新谋教授诞辰100周年[J]. 数学物理学报, 2010, 30(5): 1292-1305.

LIU Pei-De. The Martingale Inequalities in Weak-type Spaces and Their Applications[J]. Acta mathematica scientia,Series A, 2010, 30(5): 1292-1305.

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