Generalized Weighted Composition Operators on Weighted Bergman Spaces

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

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.     

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.     

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.     

Order Bounded Weighted Composition Operators Mapping into the Bergman Space

We will investigate the order boundedness of weighted composition operators ${uC_{\varphi}}$ from weighted Bergman spaces ${L_{a}^p(dA_{\alpha})}$ , weighted-type spaces ${H_{\alpha}^{\infty}}$ or Bloch-type spaces ${\mathcal{B}_{\alpha}}$ into the space ${L_{a}^q(dA_{\beta})}$ .     

Reproducing Kernel Hilbert Spaces Supporting Nontrivial Hermitian Weighted Composition Operators

We characterize those generating functions ${k(z) = \sum_{j=0}^\infty z^j/\beta(j)^2}$ that produce weighted Hardy spaces H ²(β) of the unit disk ${\mathbb D}$ supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the “classical reproducing kernels” ${z \mapsto (1 - \bar{w}z)^{-\eta}}$ , where ${w \in \mathbb D}$ and η > 0, as well as certain natural extensions of these spaces, are precisely those that are hospitable to Hermitian weighted composition operators. It also leads to a refinement of a necessary condition for a weighted composition to be Hermitian, obtained recently by Cowen, Gunatillake, and Ko, into one that is both necessary and sufficient.     

Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

The essential norm of weighted composition operators on weightedBanach spaces of analytic functions is computed in terms ofthe weights and the inducing symbols. As a consequence the boundednessand compactness of these operators is characterized. As anotherconsequence the essential norm of composition operators on weightedBloch spaces is obtained and, consequently, the boundednessand compactness of composition operators on these spaces isalso characterized. Particular instances of weighted Bloch spacesare the Lipschitz spaces. The method used allows a unified treatmentof the problem of boundedness and compactness on these spaces.     

有界对称域上不同加权Bergman空间之间的复合算子

我们研究了Cn中有界对称域Ω上不同加权Bergman空间之间的复合算子,给出了有界和紧的复合算子C(?):Lαp(Ω,dvα)→Lαq(Ω,dvβ)(0相似文献   

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．     

Cn中有界对称域上不同加权Bergman空间之间的复合算子

本文研究了Cn中有界对称域Ω上不同加权Bergman空间之间的复合算子,引入了η-αCarleson测度,利用它作为工具给出了有界的或紧的复合算子Cφ:Lαp(Ω,dνα)Lαq(Ω,dνβ)的特征.     

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．     

Generalized Interpolation in Bergman Spaces and Extremal Functions

In a recent paper A. Schuster and K. Seip [SchS] have characterized interpolating sequences for Bergman spaces in terms of extremal functions (or canonical divisors). As these are natural analogues in Bergman spaces of Blaschke products, this yields a Carleson type condition for interpolation. We intend to generalize this idea to generalized free interpolation in weighted Bergman spaces B^{p, α} as was done by V. Vasyunin [Va1] and N. Nikolski [Ni1] (cf.also [Ha2]) in the case of Hardy spaces. In particular we get a strong necessary condition for free interpolation in B^{p, α} on zero–sets of B^{p, α}–functions that in the special case of finite unions of B^{p, α}–interpolating sequences turns out to be also sufficient.     

Weighted Composition Operators Between Weighted Bloch Type Spaces and Weighted Banach Spaces of Holomorphic Functions

Let φ: 𝔻 → 𝔻 and ψ: 𝔻 → ? be analytic maps. They induce a weighted composition operator ψ C _φ acting between weighted Bloch type spaces and weighted Banach spaces of holomorphic functions. Under some assumptions on the weights, we give a necessary as well as a sufficient condition when such an operator is bounded resp. compact.     

Topological Structure of the Set of Weighted Composition Operators on Weighted Bergman Spaces of Infinite Order

We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H^∞) and L(H^∞_v) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.     

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.     

单位球的Bergman空间上Schatten类加权复合算子

本文研究了单位球的Bergman空间上Schatten类加权复合算子,得到了这种加权复合算子属于Schatten-Von Neumann.理想S_p的几个充要条件.作为推论给出了Wφ,φ是一个Hilbert- Schmidt算子的充要条件是∫_(Bn)(|ψ(ω)|~2)/((1-|φ(ω)|~2)~(n 1)dV(ω)<∞..     

Weighted Composition Operators on the Space of Bounded Harmonic Functions

We determine the norm and the essential norm of the difference of weighted composition operators on the space of bounded harmonic functions on the open unit disk. The argument is done on the boundary.     

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A2α(Ω)上的Schatten-P类加权复合算子

刻画加权Bergman空间A2α(Ω)上的加权复合算子Cψ,ψ的Schatten-p类.