变指数空间上的变指标分数次积分交换子.pdf

分类号： 密级：公开
学校代码：11065 学号：2015020207
学术硕士学位论文
变指数空间上的变指标分数次积分交换子
作者姓名 姚俊卿
指导教师 赵凯 教授
学 科 应用数学
培养单位 数学与统计学院
答辩日期 2017 年 5 月 19 日
7
摘 要
首先介绍了变指标的分数次积分算子及其交换子的基本概念及性质. 然后 , 利用变指
标分数次积分算子在变指数Morrey空间上的有界性结果, 基于Lipschitz函数的特征, 证明
了变指标分数次积分算子与Lipschitz函数生成的交换子在变指数Herz-Morrey空间中的有
界性. 最后 , 应用变指数Herz-Hardy空间上的原子分解定理, 利用H¨older不等式和Jensen不
等式, 讨论了变指标的齐性分数次积分算子及其交换子在变指数Herz-Hardy空间上的有界
性.
关键词: 变指标分数次积分; 交换子; Lipschitz函数; Herz-Hardy空间; 有界性
Abstract
In this thesis, we introduced the definitions and basic properties of the variable frac-
tional integral operators and its commutators. Then, by the boundedness of variable frac-
tional integral operators on Morrey spaces with variable exponents, using the properties of
Lipschitz functions, the boundedness of the commutators generated by variable fractional
integral operators and Lipschitz functions is obtained. Finally, based on the atomic decom-
position of Herz-Hardy spaces with variable exponents, we discussed the boundedness of
variable fractional integral operators with homogeneous kernel and its commutators on the
Herz-Hardy spaces with variable exponents.
Key words: variable fractional integral; commutator; Lipschitz function; Herz-
Hardy space; boundedness
目录
引引引言言言 ························································································ 1
第第第一一一章章章 基基基础础础知知知识识识 ····································································· 5
基本记号和概念 ··································································· 5
基本引理及证明 ··································································· 7
第第第二二二章章章 变变变指指指数数数Herz-Morrey空空空间间间上上上的的的分分分数