半平面函数空间上复合算子的差分

本文刻画半平面Korenblum空间上复合算子差分的有界性、紧性和序有界性,并探究复合算子差分的相应性质在半平面Bergman空间与Korenblum空间之间的差异性.     

WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACE AND APPLICATIONS

本文研究了单位圆盘上 Bergman空间上的加权复合算子和复平面的单连通域(不是全平面)上Bergrnan空间上的复合算子的有界性和紧性.利用复分析方法,获得了有界性与紧性的一些充分条件和必要条件,推广了Hardy空间上的若干相关结果.     

单位球上加权Bergman空间上加权复合算子的本性范数

本文给出了单位球上加权Bergman空间上的加权复合算子的本性范数,并刻画了这类加权复合算子的有界性和紧性.     

H∞和Bergman空间之间的加权复合算子

本文研究H∞和Bergman空间之间加权复合算子uCφ的有界性或紧性,利用泛函分析及复分析的方法,获得了uCφ是有界算子或紧算子的充要条件在H∞和Bergman空间之间的范数估计,推广了各类解析函数空间上加权复合算子的相应理论.     

μ-Bergman空间到Zygmund型空间的加权复合算子

本文研究了单位圆盘D上的μBergman空间到Zygmund型空间的加权复合算子的有界性和紧性问题.利用泛函分析多复变的方法,获得了单位圆盘上μ-Bergman空间到Zygmund型空间的加权复合算子为有界算子和紧算子的充要条件.     

Bergman型空间到Bers型空间之加权复合算子

讨论了Bergman型空间H(p,μ)到Bers型空间H_β~∞、小Bers型空间H_(β,0)~∞上的加权复合算子,给出了加权复合算子有界性、紧性、弱紧性的充要条件,以及紧复合算子的角导数准则.本文还讨论了具有闭值域的加权复合算子,得到了一个充分条件.     

推广的Volterra复合算子的本性范数（英文）

本文研究单位圆盘上Bergman型空间到Zygmund型空间上的一类推广的Volterra复合算子.利用符号函数φ和g刻画这类算子的有界性、紧性,并计算其本性范数.     

单位球上加权Bergman空间到?_μ型空间的加权Cesàro算子

该文利用泛函分析以及多复变的方法,研究了单位球B上加权Bergman空间到?_μ型空间的加权Cesaro算子的有界性和紧性问题.获得了单位球上加权Bergman空间到?_μ型空间的加权Cesaro算子为有界算子和紧算子的充要条件.     

Bergman空间上复合算子的紧性刻划

研究了C^n中有界强拟凸Ω上Bergman空间A^p(Ω)上的复合算子的有界性、紧性，给出了复合算子Cψ：A^p(Ω)→A^p(Ω)紧性的一个完整刻划。     

加权Bergman空间到Zygmund空间的广义复合算子

术文讨论了加权Bergman空间到Zygmund空间（小Zygmund空间）的广义复合算子Cφ^h的有界性和紧性特征,得到了以下约结果：（1）Cφ^h是加权Rergman空间到Zygmund空间的有界算子和紧算子的充要条件;（2）Cφ^h是加权Bergman空间到小Zygmund空间的有界算子和紧算子的充要条件．     

Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space

In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.     

单位球上的对偶Toeplitz算子

本文研究了单位球Bergman空间的直交补上的对偶Toeplitz算子的代数性质,首先我们给出了对偶Toeplitz算子的有界性和紧性的完全刻画,然后给出对偶Toeplitz算子的谱性质,最后证明了不存在以有界全纯或者反全纯函数为符号的拟正规对偶Toeplitz算子.     

Essential norms of weighted composition operators from weighted Bergman space to mixed-norm space on the unit ball

In this paper, we characterize the boundedness and compactness of the weighted composition operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.     

Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball

We investigate the weighted composition operator from the weighted Bergman space into the weighted Hardy space on the unit ball. As a consequence of the investigation, we also give a characterization for the boundedness and compactness of the operator whose the target space is the Hardy space.     

Riemann-Stieltjes Operators on Weighted Bloch and Bergman Spaces of the Unit Ball

Riemann–Stieltjes integrals are considered as linear operatorson weighted Bloch and Bergman spaces of the open unit ball inseveral complex variables. For weighted Bloch spaces, boundedness,compactness and weak compactness of Riemann–Stieltjesoperators are characterized by means of certain growth propertiesof holomorphic symbols. For weighted Bergman spaces, some criteriaare given for Riemann–Stieltjes operators with holomorphicsymbols to be bounded, compact and of Schatten–von Neumann'sideal.     

Compact Differences of Composition Operators over Polydisks

Moorhouse characterized compact differences of composition operators acting on a weighted Bergman space over the unit disk of the complex plane. She also found a sufficient condition for a single composition operator to be a compact perturbation of the sum of given finitely many composition operators and studied the role of second order data in determining compact differences. In this paper, based on the characterizations due to Stessin and Zhu, of boundedness and compactness of composition operators acting from a weighted Bergman space into another, we obtain the polydisk analogues of Moorhouse’s results through a different approach in main steps. In addition we find a necessary coefficient relation for compact combinations which was first noticed on the disk by Kriete and Moorhouse.     

A reproducing kernel thesis for operators on Bergman-type function spaces

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and more generally to weighted Fock spaces.     

Composition operators acting on holomorphic Sobolev spaces

We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

     

WEIGHTED COMPOSITION OPERATORS BETWEEN BERS-TYPE SPACES AND BERGMAN SPACES

This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.