取值于Banach空间内的一些函数空间上的逼近问题

发布时间：2018-09-10 09:58

【摘要】：本文研究了取值于Banach空间的一些变指标函数空间上的逼近性质.主要内容如下:第一章为文献综述、定义、记号和主要结果概述.在第二章,我们研究Bochner-Lebesgue空间相对欧式空间的Minkowski范数的的最佳同时逼近.先给出了距离的刻画,然后证明其函数取值于一个闭的可分子空间的Bochner-Lebesgue空间的最佳同时逼近性等价于此闭的可分子空间的最佳同时逼近性.在第三章,证明了取值于Banach空间的变指标大Bochner-Lebesgue空间上的逼近性质.首先,我们估计了f到和Lp(·),φ(A,Y)的距离.然后可以得到Y在X中是可近性与Lp(·)，φ(A，Y)在Lp(·)，，φ(A,X)中是可近性的等价关系.最后我们将证明Lp(·),φ(A,Y)在Lp(·),φ(A,X)中的逼近性与L1(A,Y)在L1(A X)中逼近性的关系.在第四章,研究了取值于Banach空间的变指标Bochner-Lebesgue空间上最佳同时逼近元.
[Abstract]:In this paper, we study the approximation properties on some variable index function spaces with values in Banach spaces. The main contents are as follows: the first chapter is literature review, definition, notation and summary of main results. In chapter 2, we study the best simultaneous approximation of Minkowski norm in Bochner-Lebesgue space relative to Euclidean space. A characterization of distance is given, and then it is proved that the best simultaneous approximation of its function in a closed Bochner-Lebesgue space is equivalent to the best simultaneous approximation of the closed molecular space. In chapter 3, we prove the approximation properties on the variable index large Bochner-Lebesgue spaces with values in Banach spaces. First, we estimate the distance between f and Lp (), 蠁 (Ay). Then we can get the equivalent relation between the accessibility of Y in X and that of Lp (), 蠁 (Ay) in Lp (), 蠁 (ax). Finally, we will prove the relation between the approximation of Lp (), 蠁 (Ay) in Lp (), 蠁 (AHX) and the approximation of L1 (Ay) in L1 (A X). In chapter 4, we study the best simultaneous approximation elements on variable index Bochner-Lebesgue spaces with values in Banach spaces.
【学位授予单位】：海南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.2

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