Parabolic composition operators on the ball

We give a classification, up to automorphisms, of parabolic linear fractional maps of the ball. We then show that this classification is very convenient to study the geometric properties of these maps, as well as the associated composition operators.     

Hankel operators on the Bergman space of the unit ball

We characterize the bounded holomorphic functions in the unit ball of for which the operator is compact. For the result was obtained by Axler and Gorkin in 1988 and by Zheng in 1989.

     

Cesàro operators on Hardy spaces in the unit ball

This article establishes the boundedness of the generalized Cesàro operator on holomorphic Hardy spaces in the unit ball. The approach consists in writing the generalized Cesàro operator as a composition of certain integral operators.     

Dynamics of weighted composition operators in the unit ball

In the present paper, we investigate the dynamic behavior of weighted composition operators acting on the space of holomorphic functions on the unit ball in ${\mathbb{C}}^N$.     

Linear fractional composition operators on the Dirichlet space in the unit ball

We investigate the adjoints of linear fractional composition operators Cφ acting on classical Dirichlet space D(BN ) in the unit ball BN of CN , and characterize the normality and essential normality of Cφ on D(BN ) and the Dirichlet space modulo constant function D0(BN ), where φ is a linear fractional map of BN . In addition, we also show that for any non-elliptic linear fractional map φ of BN , the composition maps σ ο φ and φ ο σ are elliptic or parabolic linear fractional maps of BN .     

Disjoint mixing composition operators on the Hardy space in the unit ball

We characterize disjoint mixing and disjoint hypercyclicity of finite many composition operators acting on the Hardy space on the unit ball.     

Integral-type operators acting between weighted-type spaces on the unit ball

Let B denote the unit ball in Cⁿ and H(B) the space of all holomorphic functions on B. We study the boundedness and compactness of the following integral-type operators

     

单位球Dirichlet空间上的交换对偶Toeplitz算子

研究对偶Toeplitz算子（半）交换时其符号的关系.通过对其符号的分解,借助多复变函数的有关理论,得到了单位球Dirichlet空间上以多重调和函数为符号的对偶Toeplitz算子Sψ与Sψ（半）交换的充要条件.     

Compact differences of composition operators on Holomorphic Function Spaces in the unit ball

We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s > 1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.     

A class of integral operators on mixed norm spaces in the unit ball

This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball. The author is supported in part by the NNSF China (No. 10671115), grants from Specialized Research Fund for the doctoral program of Higher Education (No. 20060560002) and NSF of Guangdong Province (No. 06105468).     

Valiron's theorem in the unit ball and spectra of composition operators

We prove a version of Valiron's conjugacy theorem for Schur class mappings of the unit ball of CN. As an application we obtain a formula for the spectral radius of composition operators on the ball with Schur class symbols.     

M-harmonic Besovp-spaces and Hankel operators in the Bergman space on the ball in ℂ n

In this paper, we characterize the Hardy class ofM-harmonic functions on the unit ballB in ℂ ⁿ in terms of the Berezin transform. We define and study the Besovp-spaces ofM-harmonic functions. For anM-harmonic symbolf, we give various criteria for the Hankel operatorsH _f andH _f to be bounded, compact or in the Schatten-von-Neumann classS _p . These criteria establish a close relationship among Besovp-spaces, Berezin transform, the invariant Laplacian, and Hankel operators on the unit ballB.     

The multiplication operators on some analytic function spaces of the unit ball

We give equivalent definitions of the multipliers of the space of functions of bounded mean oscillation, the Bloch space and their logarithmic counterparts.     

Asymptotic behavior of resolvents of coaccretive operators in the Hilbert ball

We study the resolvents of coaccretive operators in the Hilbert ball, with special emphasis on the asymptotic behavior of their compositions and metric convex combinations. We consider the case where the given coaccretive operators share a common fixed point inside the ball, as well as the case where they share a common sink point on its boundary. We establish weak convergence in the former case and strong convergence in the latter. We also present two related convergence results for a continuous implicit scheme.