数学物理学报 ›› 2010, Vol. 30 ›› Issue (5): 1292-1305.

• 论文 • 上一篇    下一篇

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

刘培德   

  1. 武汉大学数学与统计学院 武汉 430072
  • 收稿日期:2010-08-22 修回日期:2010-09-22 出版日期:2010-10-25 发布日期:2010-10-25
  • 基金资助:

    国家自然科学基金(10671147)资助

The Martingale Inequalities in Weak-type Spaces and Their Applications

 LIU Pei-De   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2010-08-22 Revised:2010-09-22 Online:2010-10-25 Published:2010-10-25
  • Supported by:

    国家自然科学基金(10671147)资助

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