| 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 |
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| 引用本文： | 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(A辑), 2010, 30(5): 1292-1305 |
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| 作者姓名： | 刘培德 |
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| 作者单位： | 武汉大学数学与统计学院 武汉 430072 |
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| 基金项目： | 国家自然科学基金(10671147)资助 |
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| 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.
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| 关 键 词： | 鞅论 原子分解 加权不等式 拟赋范空间 |
| 收稿时间： | 2010-08-22 |
| 修稿时间： | 2010-09-22 |
The Martingale Inequalities in Weak-type Spaces and Their Applications |
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| LIU Pei-De. The Martingale Inequalities in Weak-type Spaces and Their Applications[J]. Acta Mathematica Scientia, 2010, 30(5): 1292-1305 |
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| Authors: | LIU Pei-De |
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| Affiliation: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072 |
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| 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. |
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| Keywords: | Martingale theoryzz Atomic decompositionzz Weighted inequalityzz Quasi-normed spacezz |
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