ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.

A Note on Weighted Composition Operators on the Fock Space

Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T （Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46： 847-856）, this paper shows that a bounded weighted composition operator onthe Fock space is a Fredholm operator if and only if it is an invertible operator, andif and only if it is a nonzero constant multiple of a unitary operator. The result isvery different from the corresponding results on the Hardy space and the Bergmanspace.

Fock-Sobolev Spaces and Weighted Composition Operators among Them

Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.

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.

WEIGHTED COMPOSITION OPERATORS ON THE HILBERT SPACE OF DIRICHLET SERIES

In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.

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.

Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains

Let BE be a bounded symmetric domain realized as the unit open ball of JB^(*)-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE)to weighted Hardy space Hv∞in terms of Kobayashi distance.The authors also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,they show that the boundedness and compactness are equivalent for composition operator fromB(BE)to H∞(BE),when is a finite dimension JB^(*)-triple.Finally,they show the boundedness and compactness of weighted composition operators from B(BE)to Hv,0∞(BE)are equivalent when is a finite dimension JB^(*)-triple.

Essential Norms of Weighted Composition Operators from Weighted Bergman Space to Mixed-norm Space on the Unit Ball

In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.

A Class of Normal Weighted Composition Operators on the Fock Space of C^n

This paper characterizes a class of normal weighted composition operators and their spectrum on the Fock space of Cn.

Weighted Composition Operators of H~∞ intoα-Bloch Spaces on the Unit Ball

In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in C^n.

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.

Weighted Composition Operators between Bergman-Type Spaces

Let g1,g2 be normal functions. For all 0 〈 p,q 〈 ∞, the necessary and sufficient conditions for weighted composition operators Tψ,φ ： A^Pg1 → A^Pg2 to be bounded or compact between Bergman type spaces on the unit ball of C^n are given.

Weighted composition operators on the Fock space

In this paper,we study weighted composition operators on theFock space F^(2).We prove that each bounded composition operator on F^(2) is complex symmetric.This is in sharp contrast with the phenomenon on the Hardy space H^(2)(D).We characterize Hermitian weighted composition operators and algebraic weighted composition operators with degree less than or equal to two on F^(2).In addition,we investigate cyclicity and hypercyclicity of complex symmetric weighted composition operators.We also characterize those weighted compositionoperators that preserveframes,tight frames or normalized tight frames on F^(2).Finally,we study mean ergodicity and uniformly mean ergodicity of weighted composition operators.

The Role of BMOA in the Boundedness of Weighted Composition Operators on the Unit Ball

We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space（resp.VMOA by the little Bloch space）.

Weighted Composition Operators between Bergman Spaces with Exponential Weights

In this paper,we study some properties of weighted composition operators on a class of weighted Bergman spaces Ap with O<p≤∝ and φ∈Wo.Also,we completely characterize the q-Carleson measure for Ap in terms of the averaging function and the generalized Berezin transform with 0<q<∝.As applications,the boundedness and compactness of weighted composition operators acting from one Bergman space A^(p)_(φ) to another Ag are equivalently described and the Schatten class property of the weighted composition operator acting on A^(2)_(φ) are given.Our main results are expressed in terms of certain Berezin type integral transforms.

A Note on Weighted Composition Operators on the Weighted Bergman Space

This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.

COMPLEX SYMMETRIC C_(0)-SEMIGROUPS ON THE WEIGHTED HARDY SPACES H_(γ)(D)

In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weighted composition conjugations A_(u,v) on H_(γ)(D):either C_(1) or C_(2).We completely characterize C_(1)-symmetric(C_(2)-symmetric)C_(0)-semigroups of weighted composition operators W_(ψ,φ) on H_(γ)(D).