广义Bergman空间上的紧复合算子

首先证明广义Bergman空间A_(N,α)~p,(α-n-1,p0)上的复合算子C_φ的有界性和紧性是不依赖于p的,进而证明了若对某个q0和-n-1βα,C_φ在A_(N,β)~α上有界,则C_φ在A_(N,α)~p,α(α-n-1,p0)上是紧的当且仅当lim|z|→1-1-(|z|~2/1-|φ(1)|~2)=0.     

单位球上Bergman空间上的紧算子

当S满足一些可积条件时,我们证明了Lap(B)(p>1)上的有界算子S是紧的当且仅当S的Berezin变换在单位球B的边界趋近于零.     

单位球加权Bergman空间上的紧算子

In this paper,we study the compact operators on weighted Bergman spaces of the unit ball.Extending Miao and Zheng’result in 2004,we obtain the necessary and sufficient conditions for the operator to be compact on weighted Bergman spaces of the unit ball under some integrable conditions.     

Compact Operators on Bergman Spaces

We prove that a bounded operator S on L _a ^p for p > 1 is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disk if S satisfies some integrable conditions. Some estimates about the norm and essential norm of Toeplitz operators with symbols in BT are obtained.     

Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball

We study the so-called radial operators, and in particular radial Toeplitz operators, acting on the standard weighted Bergman space on the unit ball in ${\mathbb{C}^n}$ . They turn out to be diagonal with respect to the standard monomial basis, and the elements of their eigenvalue sequences depend only on the length of multi-indexes enumerating basis elements. We explicitly characterize the eigenvalue sequences of radial Toeplitz operators by giving a solution for the weighted extension of the classical Hausdorff moment problem, and show that the norm closure of the set of all radial Toeplitz operators with bounded measurable radial symbols coincides with the C*-algebra generated by these Toeplitz operators and is isomorphic and isometric to the C*-algebra of sequences that slowly oscillate in the sense of Schmidt.     

加权Bergman空间上的紧算子

本文讨论了加权Ｂｅｒｇｍａｎ空间上的Ｔｏｅｐｌｉｔｚ算子,证明了Ｔｏｐｌｉｔｚ算子的有限乘积的有限和是紧的当且仅当它的Ｂｅｒｅｚｉｎ变换在边界上趋向于零．     

Compact Operators on the Bergman Spaces of the Unit Ball and the Polydisk in C^n

Let Ω be the unit ban or the polydisk of C^n and La^2 (Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on La^2 (Ω), then S is compact if and only if the Berezin transform S↑-(z) of S tends to zero as z→эΩ.     

Closed-Range Composition Operators on Weighted Bergman Spaces

For analytic self-maps φ of the unit disk, we show that recently given conditions that are both necessary and sufficient for the composition operator C _φ to be closed-range on the classical Bergman space \mathbbA²{\mathbb{A}^2} are actually necessary and sufficient in the general setting of the weighted Bergman spaces \mathbbA^p_a{\mathbb{A}^p_{\alpha}} , for 1 ≤ p < ∞ and weights of the form (1 - |z|²)^a{(1 - |z|^2)^{\alpha}} ; where α > −1. Along the way, we show how work done in a paper of J. Akeroyd, P. Ghatage and M. Tjani can be used to improve upon the most definitive of these conditions, and we give applications.     

Bergman空间和q-Bloch空间之间的复合算子

本文讨论了Bergman空间和q-Bloch空间(小q-Bloch空间)之间的复合算子C(ψ)的有界性和紧性特征,得到了以下结论(1)C(ψ)是q-Bloch空间(小q-Bloch空间)到Bergman空间的有界算子或紧算子之充要条件;(2)C(ψ)是Bergman空间到q-Bloch空间的有界算子或紧算子之充要条件;(3)C(ψ)是Bergman空间到小q-Bloch空间的有界算子或紧算子之充要条件,还给出了算子C0的范数估计,此处C0(f)(z)=fo(ψ)(z)-f((ψ)(0)).     

Compact Hankel Operators on Generalized Bergman Spaces of the Polydisc

Let ${\vartheta}$ be a measure on the polydisc ${\mathbb{D}^n}$ which is the product of n regular Borel probability measures so that ${\vartheta([r,1)^n\times\mathbb{T}^n) >0 }$ for all 0 < r < 1. The Bergman space ${A^2_{\vartheta}}$ consists of all holomorphic functions that are square integrable with respect to ${\vartheta}$ . In one dimension, it is well known that if f is continuous on the closed disc ${\overline{\mathbb{D}}}$ , then the Hankel operator H _f is compact on ${A^2_\vartheta}$ . In this paper we show that for n ≥ 2 and f a continuous function on ${{\overline{\mathbb{D}}}^n}$ , H _f is compact on ${A^2_\vartheta}$ if and only if there is a decomposition f = h + g, where h belongs to ${A^2_\vartheta}$ and ${\lim_{z\to\partial\mathbb{D}^n}g(z)=0}$ .     

Bergman空间和q-Bloch空间之间的复合算子

本文讨论了Bergman空间和q-Bloch空间(小q-Bloch空间)之间的复合算子Cφ的有界性和紧性特征,得到了以下结论:(1)Cφ是q-Bloch空间(小q-Bloch空间)到Bergman空间的有界算子或紧算子之充要条件; (2)Cφ是Bergman空间到q-Bloch空间的有界算子或紧算子之充要条件; (3)Cφ是Bergman空间到小q-Bloch空间的有界算子或紧算子之充要条件,还给出了算子 Cφ0的范数估计,此处Cφ0(f)(z)=foφ(z)-f(φ(0))．     

加权Begman空间的加权复合算子的本性模

利用上极限,给出了单位球上加权Bergman空间的加权复合算子的本性模的表示．     

Weighted Composition Operators on Bergman and Dirichlet Spaces

Let H() denote a functional Hilbert space of analytic functions on a domain . Let w : C and : be such that w f is in H() for every f in H(). The operator wC given by f w f is called a weighted composition operator on H(). In this paper we characterize such operators and those for which (wC )* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces.     

Generalized Weighted Composition Operators on Weighted Bergman Spaces

The boundedness and compactness of the generalized weighted composition operator on weighted Bergman spaces are discussed.     

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.     

Compact Differences of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Let be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings and which characterize the compactness of differences of two weighted composition operators on the space . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.      

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．     

加权Bergman空间到μ-Bloch空间的复合算子

给定α＞-1,p＞0和[0,1)上的正规函数μ,得到了Cn中单位球上加权Bergman空间Apα到μ-Bloch空间βμ的复合算子C(ψ)为有界算子和紧算子的充要条件,同时也给出了几个推论.     

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.