【作者】 张亮；

【导师】 周泽华；

【作者基本信息】 天津大学 ， 应用数学， 2012， 硕士

【摘要】 解析函数空间上的复合算子的代数性质是算子理论的重要组成部分.本文主要研究了一些函数空间上的积分算子与复合算子的本性交换性,加权微分复合算子的有界性和紧性,以及积分算子与复合算子乘积的差分的本性范数等价估计等.本文共分为五章来详细论述上述问题：第一章为绪论部分,主要介绍了近些年研究本文涉及的一些算子得到的结果及其发展情况,并在已有的结果的基础上,阐述本文所进行的证明.第二章为预备知识部分,主要介绍本文所用到的一些基本概念和基本性质.第三章主要给出了单位圆盘D上从H(p,q,γ)到Bα的积分算子与复合算子的本性可交换的性质.第四章主要给出了单位圆盘D上从Bergman空间到ωμ(n)空间的加权微分复合算子的有界性和紧性的充分必要条件.第五章主要给出了单位球上的从H(p,q,γ)空间到Bμ空间的积分算子和复合算子乘积的差分的有界性,并且给出了其本性范数的等价估计.更多还原

【Abstract】 Algebraic properties of composition operators in analytic function spaces are im-portant component parts in operator fields. In this paper, we characterize essential commutativity of the integral operators and composition operators, the boundedness and compactness of the weighted differentiation composition operator, and some asymp-totically equivalent expressions of the essential norms of difference of products of the integral type and composition operators in some analytic function spaces.The paper is mainly divided into five chapters.The first chapter is the introduction of the whole paper. We talk about the back-ground of this paper, and make plans for the research of the problem.Next chapter of the paper, some important concepts and lemmas which are related to the article are given. They are the foundations and tools of the later work, and we will use them without proof.The third chapter discusses the properties of essential commutativity of the integral operators and composition operators from the mixed-norm space to the Bα space in the unit disk.The fourth chapter characterizes the boundedness and compactness of the weighted differentiation composition operator from weighted Bergman space to n-th weighted space on the unit disk of C.At last, we characterizes the boundedness of the differences of the products of integral operators and composition operators from the mixed-norm space to μ-Bloch type space on the unit ball of Cn. At the same time, some asymptotically equivalent expressions of the essential norms of difference of products of integral operators and composition operators are presented.更多还原