Orlicz空间的强凸点和H_μ性质

发布时间：2018-02-02 14:50

本文关键词： Banach空间 Orlicz空间 H_μ性质 (弱)强凸点 (弱)紧强凸点　出处：《哈尔滨理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要对Banach空间和Orlicz空间的一些点态性质和几何性质进行了研究。全文共分三章,主要研究如下:第一章是绪论,主要介绍了Banach空间和Orlicz空间理论的发展历史和背景,然后阐述了研究Banach空间中点态性质和几何性质的意义,并给出本文研究的主要内容。第二章研究Orlicz空间中强凸点的刻画问题。首先将Banach空间的一些几何性质点态化,引入弱强凸点和弱紧强凸点的概念,讨论它们与强凸点、紧强凸点、局部一致凸点、强光滑点、H点、WM点、强U点、S点等之间的关系。然后研究了强凸点在一类具体的Banach空间——Orlicz空间中的刻画问题。根据Banach空间中强凸点与强端点之间的关系,我们得出了强凸点在赋Luxemburg范数的Orlicz函数空间和Orlicz序列空间的等价刻画,作为推论给出了这些空间具有强凸性质的充要条件。第三章研究赋p-Amemiya范数的Orlicz函数空间的H_μ性质。讨论了赋p-Amemiya范数的Orlicz函数空间L_(M,P)中依测度收敛的H性质和△_2-条件之间的关系。证明了若Orlicz函数M仅在零点为零,则赋p-Amemiya范数的Orlicz函数空间L_(M,P)具有H_μ性质的充分必要条件为M对所有的实数满足△_2-条件而且M是有限值的;如果Orlicz函数M不仅在零点为零,则L_(M,P)具有H_μ性质的充分必要条件为M在无穷远处满足△_2-条件而且M是有限值的。对于Orlicz函数空间L_(M,P)的子空间E_(M,P),我们也给出了类似的结论。
[Abstract]:In this paper, some pointwise properties and geometric properties of Banach space and Orlicz space are studied. The thesis is divided into three chapters. The main research is as follows: the first chapter is the introduction. This paper mainly introduces the history and background of Banach space and Orlicz space theory, and then expounds the significance of studying the point state property and geometric property in Banach space. In chapter 2, we study the characterization of strong convex points in Orlicz spaces. Firstly, some geometric properties of Banach spaces are pointwise. The concepts of weak strong convex point and weakly compact strong convex point are introduced, and they are discussed with strong convex point, compact strong convex point, locally uniformly convex point, strong smooth point and strong U point. Then, we study the characterization of strongly convex points in a class of concrete Banach spaces. According to the relations between strong convex points and strong endpoints in Banach spaces, we study the relations between strongly convex points and strong endpoints. Yes. We obtain the equivalent characterizations of strong convex points in Orlicz function spaces with Luxemburg norm and Orlicz sequence spaces. A necessary and sufficient condition for these spaces to have strong convexity is given as a corollary. In chapter 3, we study the H _ 渭 properties of Orlicz function spaces with p-Amemiya norm and discuss the properties of Orlicz function spaces with p-Amemiya norm. The Orlicz function space of a norm L _ s. M. It is proved that the Orlicz function M is zero only at 00:00. Then the Orlicz function space with p-Amemiya norm L _ s / M _ p) has the property of H _ 渭 if and only if M satisfies 2-condition for all real numbers and M is of finite value; If the Orlicz function M is not only zero at 00:00, then L _ S _ M. P) A sufficient and necessary condition for the property of H _ 渭 is that M satisfies the 2-condition of M at infinity and M is of finite value. We have come to a similar conclusion, Pang.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177

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