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.     

Hankel Operators on Weighted Fock Spaces

We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator spaces, fixed points of completely contractive mappings, Toeplitz operators, dynamical systems and similarity orbits of group representations.     

Norm Estimates for Weighted Composition Operators on Spaces of Holomorphic Functions

This paper shows that the boundedness of a weighted composition operator on the Hardy–Hilbert space on the disc or half-plane implies its boundedness on a class of related spaces, including weighted Bergman spaces. The methods used involve the study of lower-triangular and causal operators.     

Toeplitz Operators with BMO Symbols on Holomorphic Besov Spaces

We study the Toeplitz operator $T^{\beta }_{\mu }$ , on the holomorphic Besov spaces $B^p_s$ in the unit ball, for complex measures $\mu $ on the unit ball. We give sufficient conditions for which $T^{\beta }_{\mu }$ is bounded. In the case of positive measures or $\textit{BMO}^{\beta }$ symbols, we obtain necessary and sufficient conditions in terms of (weighted) Berezin transform and Carleson measures for Besov spaces.     

On Weighted Spaces of Harmonic and Holomorphic Functions

Weighed spaces of harmonic and holomorphic functions on theunit disc are studied. We show that for all radial weights whichare not decreasing too fast the space of harmonic functionsis isomorphic to c₀. For the weights that we consider we completelycharacterize those spaces of holomorphic functions which areisomorphic to c₀. Moreover, we determine when the Riesz projection,mapping the weighted space of harmonic functions onto the correspondingspace of holomorphic functions, is bounded.     

Differences of Composition Operators between Weighted Banach Spaces of Holomorphic Functions on the Unit Polydisk

We consider differences of composition operators between given weighted Banach spaces H ^∞ _v or H ⁰ _v of analytic functions defined on the unit polydisk D ^N with weighted sup-norms and give estimates for the distance of these differences to the space of compact operators. We also study boundedness and compactness of the operators. This paper is an extension of [6] where the one-dimensional case is treated. Received: May 15, 2007. Revised: October 8, 2007.     

Closed Range Composition Operators on Besov Type Spaces

Let $\varphi $ be a holomorphic self-map of the unit disk $\mathbb D $ . Necessary and sufficient conditions for a closed range composition operator $C_\varphi $ on Besov spaces $B_p$ and more generally on Besov type spaces $B_{p, \alpha }$ are given. An important ingredient is a reverse type Carleson condition due to Luecking.     

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.     

The Essential Norm of Hankel Operators on the Weighted Bergman Spaces with Exponential Type Weights

Let denote the closed subspace of consisting of analytic functions in the unit disc . For certain class of subharmonic functions and , it is shown that the essential norm of Hankel operator is comparable to the distance norm from H_f to compact Hankel operators.     

加权Bergman空间上小Hankel算子的Schatten类

讨论了 C\+n 中有界对称域的加权Bergman空间上符号属于 L\+2\-a(Ω, dV\-λ) 的小Hankel算子, 利用符号 Φ 的某种积分变换,给出了小Hankel算子 h\-Φ 属于Schatten理想 S\-p 的特征.     

Boundedness of Product Type Pseudodifferential Operators on Spaces of Besov Type

In this paper we consider pseudodifferential operators associated with symbols satisfying estimates of product type, and give some sufficient conditions for the operators to be bounded on BESOV spaces and on TRIEBEL —LIZORKIN spaces of product type corresponding to the above estimates. In the proof we use the characterization of these spaces by approximation by entire functions.     

Volterra Type and Weighted Composition Operators on Weighted Fock Spaces

Bounded and compact product of Volterra type integral and composition operators acting between weighted Fock spaces are described. We also estimate the norms of these operators in terms of Berezin type integral transforms on the complex plan ${\mathbb{C}}$ . All our results are valid for weighted composition operators acting on the class of Fock spaces considered under appropriate interpretation of the weights.     

Bloch型空间上的广义Volterra型算子的有界性

通过研究Bloch型空间Bα的一些性质,给出了广义复合算子Tφ,g在Bloch型空间Bα(0<α<∞)上有界的充要条件.     

Singular Integral Operators on Besov Spaces

Summary. We introduce generalized BESOV spaces in terms of mean oscillation and weight functions, following a recent work of Dorronsoro, and study the continuity of singular integral operators on them. Relations between these spaces and the BESOV spaces in terms of modulus of continuity are also studied. An application to pseudo-differential operators is given.     

Toeplitz Operators on Analytic Besov Spaces

We characterize complex measures μ on the unit disk for which the Toeplitz operator T _μ is bounded or compact on the analytic Besov spaces B _p with 1 ≤ p < ∞. Research supported in part by NSF grant, DMS 0200587 (first author); and by a NSERC grant (third author).     

广义Fock空间上的Hankel算子

利用有界(消失)平均振荡函数的性质,本文刻画了一类广义Fock空间上的Hankel算子的有界性(紧性),同时,还刻画了换位子[M_f,P]的有界性和紧性,其中P是一个Toeplitz投影算子,而M_f表示符号为f的乘子.最后,应用Berezin变换来研究了BMO空间和VMO空间的几何性质.     

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.