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.

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.

COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.

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.

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.

EQUIVALENCES BETWEEN BLOCH TYPE SPACES AND BMO SPACES ON THE HYPERBOLIC DOmAINS IN C

For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only if C(Ω)=inf{Z_o(z)·δ_o(z)·z≡Ω}>0,Also some applica- lions to automorphic function are considered.

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 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）.

Closed Range Composition Operators on a General Family of Function Spaces

In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F（p,q,s） and more generally on α-Besov type spaces F（p,αp-2,s） are given. We give a Carleson measure characterization on F （p, αp - 2, s） spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of CФ on F（p,q,s） and F（p,αp- 2,s） spaces.

Some Characterizations of Bloch Functions

We define Bloch-type functions of C;（D） on the unit disk of complex plane C and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator C;acting between two Bloch-type spaces.These obtained results generalize the corresponding known ones to the setting of C;（D）.

加权Bergman空间到Bloch空间的Volterra积分算子

本论文主要讨论从 B´ekoll´e 权诱导的 Bergman 空间 Aωp到 Bloch 空间 B 的Volterra 积分算子的有界性和紧性刻画。

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,

Multipliers and Cyclic Vectors in Bloch Type Spaces

In this paper we study the coefficient multipliers, pointwise multipliers and cyclic vectors in the Bloch type spaces B^! and little Bloch type spaces $B^\alpha_0$ for 0 < ! < X. We give several full characterizations of the coefficient multipliers (B^!, B^#) and ($B^\alpha_0,$ $B^\beta_0$) for 0 < !, # < X and pointwise multipliers M (B^!, B^#) and M ($B^\alpha_0,$ $B^\beta_0$) for 1 p !, # ] (0, X). We also obtain some properties of cyclic vectors for Bloch type spaces.

Composition Operators on Dirichlet Spaces and Bloch Space

In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.

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）.

Carleson Measure Characterization of Bloch Functions

We give several equivalences of Bloch functions and little Bloch funetions.Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions,that is,f ∈ B if and only if |Dβf（z）|p（1-|z|2）βp-1dm（z）is a generalized Carleson measure; f ∈ B0 if and only if |Dβf（z）|p（1-|z|2）βp-1dm（z）is a generalized vanishing Carleson measure,where Dβf（β】0）is the fractional derivative of analytic function f of order β,m denotes the normalised Lebesgue measure.

Difference of Composition Operators on Some Analytic Function Spaces

For two analytic self-mapsφandψdefined on the unit disk D,we characterize completely the boundedness and compactness of the difference Cφ-Cψof the composition operators Cφand Cψfrom Bloch space B into Besov space Bν∞.Moreover,we also give a complete characterization of the compactness of the difference Cφ-Cψon BMOA space.