【作者】 陈亮；

【导师】 吐尓德别克；

【作者基本信息】 新疆大学 ， 基础数学， 2010， 硕士

【摘要】 原子分解方法在鞅论及调和分析中是一种应用广泛的方法.通过对鞅进行原子分解可建立起鞅空间之间的相互联系.本文研究复拟Banach空间值Hardy鞅的原子分解,建立了Hardy鞅空间的嵌入关系,所得结果刻画了复拟Banach空间的解析q一致凸性.本文共分三章,其行文结构安排如下:第一章回顾了鞅空间理论和原子分解方法的发展历程.第二章介绍了鞅论中的一些基本概念,包括鞅,停时,原子,Hardy鞅,解析q一致凸性等.第三章给出了复拟Banach空间值Hardy鞅的原子分解定理,刻画了复拟Banach空间的解析q一致凸性,并给出了两个Hardy鞅空间的嵌入关系.更多还原

【Abstract】 As a useful tool,the atomic decomposition method plays an important part in harmonicanalysis and martingale theory.By the atomic decomposition of martingale,we can establish therelationships between martingale spaces.To martingales with Banach-space value,the results aretightly related to the geometry properties and structure of the spaces in which the martingalestake value.In this paper,we study the atomic decomposition of Hardy martingales with values incomplex quasi-Banach space and discuss the embedding relationships between Hardy martin-gale spaces.The results characterize the analytic q-uniform convexity of complex quasi-Banachspace.This thesis consists of three chapters. In chapter 1,the history of martingale spaces the-ory and atomic method is introduced.In chapter 2,some basic conceptions are described, suchas martingale,stopping time,atom,Hardy martingale,analytic q-uniform convexity,and so on.Inchapter 3,we establish several theorems about the atomic decomposition of Hardy martingalewith value in complex quasi-Banach space and characterize the analytic q-uniform convexityof complex quasi-Banach space.The embedding relationships between two Hardy martingalespaces is given at the end of chapter 3.更多还原