| UMD空间及其应用 |
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| 引用本文： | 刘培德. UMD空间及其应用[J]. 应用泛函分析学报, 2002, 4(3): 280-288 |
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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,湖北,430072 |
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| 基金项目： | 国家自然科学基金(201980233) |
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| 摘 要： | UMD空间是被广泛研究的一类新型的Banach空间，它具有一系列良好的几何性质与分析性质并且与向量值调和分析、随机分析有着广泛深刻的联系。本扼要介绍这类空间的有关问题，主要是以下几个方面：（1）引言（定义与产生背景）；（2）UMD空间的几何特性与分析特征；（3）此类空间的例；（4）在向量值调和分析理论中的应用；（5）关于鞅不等式的最优系数问题。
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| 关 键 词： | Banach空间理论 UMD空间 鞅论 向量值调和分析 最优不等式 |
| 文章编号： | 1009-1327(2002)03-0280-09 |
| 修稿时间： | 2002-08-25 |
UMD Space and Its Applications |
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| LIU Pei-deCollege of Mathematics and Statistics,Wuhan Univ. Wuhan Hubei ,China. UMD Space and Its Applications[J]. Acta Analysis Functionalis Applicata, 2002, 4(3): 280-288 |
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| Authors: | LIU Pei-deCollege of Mathematics Statistics Wuhan Univ. Wuhan Hubei China |
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| Affiliation: | LIU Pei-deCollege of Mathematics and Statistics,Wuhan Univ. Wuhan Hubei 430072,China |
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| Abstract: | The UMD spaces have been studied extensively in recent years, it is a new class of Banach spaces. Many facts show that it has many nice geometric and analytic properties, and serial applications in vector-valued harmonic analysis and stochastic analysis. In this paper, some results related to UMD space have been introduced, it carries on in the following aspects:(1) Introduction ) (2) Geometrical and analytic characterizations of UMD space; (3) UMD spaces in analysis; (4)Applications in the theory of vector-valued harmonic analysis) (5) Applications in the problems of sharp inequalities. |
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| Keywords: | Banach space theory UMD space vector-valued harmonic analysis martingale theory sharp inequality |
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