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.     

Essential norms of weighted composition operators on Müntz spaces

In this paper, we discuss the problem of compactness for weighted composition operators, defined on a Müntz space . We compute the essential norm of such operators on the Müntz spaces. As a corollary, we obtain the exact values of essential norms of composition and multiplication operators.     

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.     

Difference of composition operators between standard weighted Bergman spaces

We obtain estimates for the norm and essential norm of the difference of two composition operators between certain Bergman spaces. In particular, a necessary and sufficient condition for boundedness and compactness of the operator is established. Finally, we give a sufficient condition for boundedness and compactness of the difference operator between Hardy spaces.     

Essential norm of composition operators between weighted Hardy spaces

An asymptotic formula for the essential norm of composition operators acting between two weighted Hardy spaces H_w1 and H_w2, where w₁ and w₂ are two admissible weight functions, is given. The boundedness of the operators is also characterized.     

Composition operators that improve integrability on weighted Bergman spaces

Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.

     

Essential norms of weighted composition operators and Aleksandrov measures

We derive exact formulas for the essential and weak essential norms of weighted analytic composition operators acting on certain function spaces in the unit disc, extending and improving earlier results due to Sarason and to Kriete and Moorhouse. Differences of composition operators are also considered. The formulas involve the Aleksandrov measures associated to the symbol of the operator. The results are based on a variant of a general method due to Weis of constructing best compact and weakly compact approximants for linear operators on L¹ spaces.     

Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces

Let ψ be a holomorphic function on the open unit disk D and φ a holomorphic self-map of D. Let C_φ,M_ψ and D denote the composition, multiplication and differentiation operator, respectively. We find an asymptotic expression for the essential norm of products of these operators on weighted Bergman spaces on the unit disk. This paper is a continuation of our recent paper concerning the boundedness of these operators on weighted Bergman spaces.     

Composition operators between Bergman and Hardy spaces

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

     

Products of weighted composition and differentiation operators into weighted Zygmund and Bloch spaces

We characterize boundedness and compactness of products of differentiation operators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.     

Besov空间到Zygmund空间上的加权复合算子

研究了单位圆盘上的Besov空间B_(p,q)到Zygmund空间Z的加权复合算子u C_φ(u∈Z),利用函数空间上的算子理论相关知识,得到了u C_φ:B_(p,q)→Z的有界性和紧性的充分必要条件.     

解析函数空间上的自伴加权复合算子

通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。     

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.     

Superposition operators between weighted spaces of analytic functions

Abstract

We study the existence and the continuity of superposition operators between weighted spaces of holomorphic functions in terms of the weights.