WEIGHTED COMPOSITION OPERATORS BETWEEN BERS-TYPE SPACES AND BERGMAN SPACES

This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.     

Bergman空间L^1a（D）上的Toeplitz和Hankel算子

本讨论了Bergman空间L^1a(D)中Toeplitz和Hankel算子的W紧性,得到与L^2a(D)上Toeplitz,Hankel算子紧性类似的某些结果。     

Bergman空间L^1a（Ω）上的Toeplitz和Hankel算子

本文讨论了Bergman空间L^1a(Ω)中Toeplitz和Hankel算子的W^*紧性,得到与L^2a(Ω)上T－H算子紧性^[4]类似的某些结果。     

ROUGH OPERATORS AND COMMUTATORS ON HOMOGENEOUS WEIGHTED HERZ SPACES

The authors esstablish the boundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions.In particular ,the Cadderon-Zygmund singular integrals and the rough R.Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.     

Bergman空间A~2上的Toeplitz与Hankel算子的紧性

本文给出Ｂｅｒｇｍａｎ空间Ａ２上的Ｔｏｅｐｌｉｔｚ算子Ｔｆ与Ｈａｎｋｅｌ算子Ｈｆ（ｆ∈Ｌ∞）是紧的充要条件，从而解决Ｓ．Ａｘｌｅｒ分别于１９８４和１９８５年提出的一个问题．     

A NOTE ON SUNSETS IN SPACES OF BOUNDED LINEAR OPERATORS

In the note the author gives a correct proof of the theorem on sunsets in spaces of bounded linear operators given in the author‘s another paper.     

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.     

（1.2） INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

1.(1.2)InverseandLocalFinePropertyofaFamilyofOperatorsTxLetEandFbebothBanachspaces,andB(E,F)thesetofallboundedlinearoperatorsfromEintoFAnoperatorT B(F,E)issaidtobea(1.2)inverseofTifTT T=TandT TT =T .IfT satisfiesonlythefirstcondition,thenT issaidtobe...     

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

The paper defines an extended Ceshro operator Tg with holomorphic symbol g in the unit ball B of C^n as Tg(f)(z) =∫^10f(tz)Rg(tz)dt/t, f∈H(B),z ∈ B. Where Rg(z) =∑^nj=1 zjθg/θzj is the radial derivative of g. In this paper, the author charac-terizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space B0.     

Composition operators induced by symbols defined on a polydisk

Suppose φ is a holomorphic mapping from the polydisk Dm into the polydisk Dn, or from the polydisk Dm into the unit ball Bn, we consider the action of the associated composition operator Cφ on Hardy and weighted Bergman spaces of Dn or Bn. We first find the optimal range spaces and then characterize compactness. As a special case, we show that if

     

Bergman空间上的复合算子的范数

本文研究了Bergman空间上的复合算子的范数与再生核的关系,证明了紧复合算子C的范数‖C‖=sup{‖C*kw‖:w∈D}的充要条件是(0)=0或是仿射映射,即(z)=sz+t,s,t是满足|s|+|t|<1的常数,其中kw为Bergman空间的规范再生核, C*是C的共轭算子.     

Composition operators on the polydisc

In this paper we study the boundedness of composition operators on the weighted Bergman spaces and the Hardy space over the polydisc ${\mathbb{D}}^n$. Studying the volume of sublevel sets we show for which n the necessary conditions obtained by Bayart are sufficient. For arbitrary polydisc we prove the rank sufficiency theorem which, in particular, provides us with a simple criterion describing boundedness of composition operators on the spaces over the bidisc. Such a consistent characterization is obtained for the classical Bergman space over the tridisc.     

Corrigendum to “On norms of composition operators acting on Bergman spaces” [J. Math. Anal. Appl. 291 (2004) 189-202]

A theorem and a corollary in the paper cited in the title were stated incorrectly, as was pointed out by Christopher Hammond. We now state correctly and prove both of them. These results still generalize and explain the geometric meaning of the Cowen-Hurst norm formula. We also include additional references and provide an example relevant for further study.     

Composition operators on a Banach space of analytic functions

In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL _α ¹ (D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range. Supported by NNSFC No.19671036     

Derivative-free characterizations of bounded composition operators between Lipschitz spaces

We prove that maps into if and only if belongs to . In the case β < 1, we give another two equivalent conditions. Supported by MNZŽS Serbia, Project No. ON144010.     

Compact differences of composition operators

A characterization of compact difference is given for composition operators acting on the standard weighted Bergman spaces and necessary conditions are given on a larger scale of weighted Dirichlet spaces. Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts. The additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component.