A DERIVATIVE-HILBERT OPERATOR ACTING FROM LOGARITHMIC BLOCH SPACES TO BERGMAN SPACES

Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=■[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the Bergman space■,where 0≤α<∞,0<p<∞.We also characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the classical Bloch space■.

CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES

For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space BLαfor allα∈R.

EXTENDED CESRO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C^n

The paper defines an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of Cn asWhere is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space Bo-

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.

ON DIRICHLET TYPE SPACES AND α-BLOCH SPACES IN THE UNIT BALL OF C^n

In this paper, the authors study the inclusion relations between Dirichlet type spaces DΥT and α-Bloch spaces βα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods. Furthermore, they sharpen one of the results when Υ=n, which proves that a conjecture in [7] is true.

COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

Let U^n be the unit polydisc of C^n and φ（φ,…,φ） a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0＊（U^n） if and only if φ ∈β0＊（U^n） for every ι=1,2,... ,n, and also gives a sufficient and necessary condition for the composition operator Cφto be compact on the little Bloch space β0＊ （U^n）.

Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.

BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

In this article, we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.

COMPOSITION OPERATORS FROM p-BLOCH SPACES TO LITTLE q-BLOCH SPACES ON THE UNIT BALL OF C^n

For all 0 〈 p, q 〈 ∞, let Cφ denote the composition operator from q-Bloch spaces βp to little p-Bloch spaces β0q on the unit ball of C^n. In this article, necessary and sufficient conditions for Cφ to be a bounded or compact operator are given.

PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES

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

Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains

In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

第二类广义华罗庚域上从α-Bloch空间到Bers型空间的加权复合算子的有界性和紧性

本文在第二类广义华罗庚域上定义了加权Bloch空间和Bers型空间,并讨论了从α-Bloch空间到Bers型空间之间的加权复合算子的有界性和紧性,得到了该加权复合算子是有界算子或紧算子的充分条件和必要条件.

从Zygmund型空间到Bloch型空间的复合算子的差分

给出复合算子的差分C_(φ)-C_(ψ):Z_(α)→B^(β)(α>1,β>0)的有界性与紧性的一些等价条件.此外,作为非平凡的拓展,利用Taylor级数和Raabe判别法构建了有界或紧的复合算子的差分C_(φ)-C_(ψ):Z_(α),0→B^_(0)(β)的等价刻画.

对数Bloch型空间上微分复合算子乘积的本性范数

目的为刻画微分复合算子乘积C_(φ)D^(m)在对数Bloch型空间上的本性范数特征。方法利用有界序列{z^(n)}∞n=1刻画对数Bloch型空间上微分复合算子乘积C_(φ)D^(m)的有界性特征,以及泛函分析中的算子理论,例如紧算子性质和对本性范数上下界的估计。结果在C_(φ)D^(m)有界的条件下,给出了微分复合算子C_(φ)D^(m)的本性范数特征,即这里m为非负正整数,微分复合算子乘积为C_(φ)D^(m)f=f(m)°φ。结论在C_(φ)D^(m)有界的条件下,则微分复合算子C_(φ)D^(m)的本性范数可由有界序列{z^(n)}∞n=1的特征刻画。

Weighted Composition Operators between Generally Weighted Bloch Spaces of Polydisk

Let φ be a holomorphic self-map of the open unit polydisk U nin C nand ψ a holomorphic function on U n,p,q0. ∨In this paper,we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and φ,sufficient conditions for the weighted composition operator Wψ,φ induced by ψ and φ to be bounded and compact between the generally weighted Bloch spaces are investigated.

Composition Operators on the Bloch Space of Several Complex Variables

In this paper,we study the boundedness and compactness of composition operator C on the Bloch space β（Ω）,Ω being a bounded homogeneous domain.For Ω=Bn,we give the necessary and sufficient conditions for a composition operator C to be compact on β（Bn）or β0（Bn）.

Compactness of Composition Operators from the Bloch Space β to Q_K Spaces

Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated,

Compact composition operators on the Bloch space in polydiscs

Let Un be the unit polydisc of ?n 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 $$\sum\limits_{k,1 = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial z_k }}(z)} \right|} \frac{{1 - |z_k |^2 }}{{1 - |\phi _l (z)|^2 }}< \varepsilon ,$$ whenever dist(φ(z), ?U n )<δ.

Composition Operators on α-Bloch Spaces of the Unit Ball

The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball.