Bloch型空间上的广义Cesàro算子

对区间[0,1)上给定的的正规权函数ω和单位圆盘D上的全纯函数Ψ,本文刻画了Bloch型空间Bω及小Bloch型空间Bω,0上广义Cesaro算子TΨ的有界性和紧性.此处(T(?)f)(z)= ∫0 z f(?)(?)'(?)ds.     

不同权Bloch型空间之间的加权Cesàro 算子

该文讨论了$\a$-Bloch空间$\ba$和对数Bloch空间$\bl$之间的加权Ces\'aro算子$\tg$的有界性和紧性,给出$\tg$是$\ba$到$\bl$的有界算子或紧算子的充要条件和$\tg$是$\bl$到$\ba$的有界算子或紧算子的充要条件.     

Bloch型空间上的广义Cesàro算子

对区间[0,1)上给定的的正规权函数ω和单位圆盘D上的全纯函数(と),本文刻画了Bloch型空间Bω及小Bloch型空间Bω,0上广义Cesàro算子T(と)的有界性和紧性.此处(T(と)f)(z)=∫z0f(と)(と)'(と)d(と).     

单位球上Bergman空间的Cesàro算子

对一切p∈(0,∞),Cesaro算子在加权的p次Bergman空间A p(Bn)上有界,但不是紧的,其中Bn是Cn上中的单位球,而是[0,1)上的正规权函数.与Cesaro算子相联系,以解析函数g为符号的积分箅子Rg定义为本文刻画了使算子Rg在A p(Bn)上是有界(或紧)的解析函数g的特征.同时,在多圆柱上也能得出类似的结果.     

C~n中Dirichlet型空间和Bloch型空间上的加权Cesàro算子

本文在Cn中单位球上讨论了Dirichlet型空间Dp,Bloch型空间βp以及Lipschitz空间Ap上加权Cesaro算子Tg的有界性和紧性.得到当P<0,q≤P 2或P>n,q≤P 2时,Tg是Dp到Dq的有界算子或紧算子的充要条件;对所有的P,q,获得了Tg是βp到βq之有界算子和紧算子的充要条件及Tg是β0p到β0q之有界算子的充要条件等.     

Cn中Dirichlet型空间和Bloch型空间上的加权Cesàro算子

本文在Cn中单位球上讨论了Dirichlet型空间Dp,Bloch型空间βp以及Lipschitz空间Λp上加权Cesàro算子Tg的有界性和紧性.得到当p＜0,q(≤) p+2或p＞n,q(≤)p+2时,Tg是Dp到Dq的有界算子或紧算子的充要条件;对所有的p,q,获得了Tg是βp到βq之有界算子和紧算子的充要条件及Tg是β0p到β0q之有界算子的充要条件等.     

Bloch空间上的Cesaro算子是有界的

记B={f:f∈H(D),‖f‖B＜∞}为Bloch空间，其中‖f‖B=sup |x|＜1(1-|z|^2)|f′(z)|,对于f(z)=^∞∑(k-0)akz^k∈B，定义Cesaro算子B为(Bf)(z)=^∞∑(n=0)(1/(n 1) ^n∑(k=0)ak)z^n在这篇文章中，我们将证明如下结果。     

Bergman型空间与Cesàro算子

本文给出了Bergman型空间的一个特征及在Bergman型空间Cesàro算子的有界性．     

Bergman型空间与Cesàro算子

本文给出了Bergman型空间的一个特征及在Bergman型空间Cesàro算子的有界性．     

加权Dirichlet空间上的一般Cesàro算子

对加权Dirichlet空间我们研究了其上一般Cesaro算子的有界性．此处H(D)表示复平面单位圆盘D上全纯函数的全体．     

Compact composition operators on the Bloch space in polydiscs

Let Uⁿ be the unit polydisc of ℂⁿ and φ=(φ₁, ⋯, φ _n ) a holomorphic self-map of Uⁿ. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Uⁿ) if and only if for every ε > 0, there exists a δ > 0, such that

On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball

We introduce the following integral-type operator on the space H(B) of all holomorphic functions on the unit ball B⊂Cn

     

Norm-attaining composition operators on the Bloch spaces

We prove that every composition operator C? on the Bloch space (modulo constant functions) attains its norm and characterize the norm-attaining composition operators on the little Bloch space (modulo constant functions). We also identify the extremal functions for ‖C?‖ in both cases.     

On the composition operators on the Bloch space of several complex variables

In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain.     

A characterization of Bloch space and Besov space

On the unit disk of the complex plane, a characterization for the membership of Bloch space and analytic Besov space is expressed extending known results.     

On a product-type operator from Bloch spaces to weighted-type spaces on the unit ball

We characterize the boundedness and compactness of a product of radial-derivative, composition and multiplication operators from Bloch spaces to weighted-type spaces on the unit ball.     

On an integral-type operator from iterated logarithmic Bloch spaces into Bloch-type spaces

Let H(B) denote the space of all holomorphic functions on the open unit ball B of Cⁿ. Let φ=(φ₁,…,φ_n) be a holomorphic self-map of B and g∈H(B) such that g(0)=0. In this paper we study the boundedness and compactness of the following integral-type operator, recently introduced by Xiangling Zhu and the second author

     

Topological structures of the sets of composition operators on the Bloch spaces

We study properties of the topological sets of composition operators on Bloch and little Bloch spaces in the operator topology.     

对数Bloch空间上积型算子的有界性

让H(D)表示复平面C里的单位圆盘D上的所有解析函数的全体,ψ_1,ψ_2∈H(D),而φ是D到D的解析自映射.本文刻画了对数Bloch空间上积型算子T_(ψ_1,ψ2,φ)的有界性.