scholarly journals Weighted Composition Operators fromF(p,q,s)Spaces toHμ∞Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Holomorphic Functions ◽  
Weighted Composition Operators ◽  
General Function ◽  
Weighted Composition ◽  
Weighted Type ◽  
General Function Space

LetH(B)denote the space of all holomorphic functions on the unit ballB. Letu∈H(B)andφbe a holomorphic self-map ofB. In this paper, we investigate the boundedness and compactness of the weighted composition operatoruCφfrom the general function spaceF(p,q,s)to the weighted-type spaceHμ∞in the unit ball.

scholarly journals Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaohong Fu ◽  
Xiangling Zhu
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weighted Composition Operators ◽  
Weighted Composition

LetBnbe the unit ball ofCn,H(Bn)the space of all holomorphic functions inBn. Letu∈H(Bn)andαbe a holomorphic self-map ofBn. Forf∈H(Bn), the weigthed composition operatoruCαis defined by(uCαf)(z)=u(z)f(α(z)),z∈Bn.The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.

scholarly journals Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Sei-Ichiro Ueki ◽  
Luo Luo
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Essential Norm ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

We estimate the essential norm of a compact weighted composition operator acting between different Hardy spaces of the unit ball in . Also we will discuss a compact multiplication operator between Hardy spaces.

Complex symmetry of weighted composition operators in several variables

2016 ◽  
Vol 27 (02) ◽  
pp. 1650017 ◽  
Author(s):  
Maofa Wang ◽  
Xingxing Yao
Keyword(s):  
Composition Operators ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
General Function ◽  
Higher Dimensional ◽  
Weighted Composition ◽  
Complex Symmetric ◽  
Symmetric Operators ◽  
Funct Anal ◽  
General Function Space

In this paper, we investigate analytic symbols [Formula: see text] and [Formula: see text] when the weighted composition operator [Formula: see text] is complex symmetric on general function space [Formula: see text]. As applications, we characterize completely the compactness, normality and isometry of complex symmetric weighted composition operators. Especially, we show that the equivalence of compactness and Hilbert–Schmidtness, and the existence of non-normal complex symmetric operators for such operators, which answers one open problem raised by Noor in [On an example of a complex symmetric composition operators on [Formula: see text], J. Funct. Anal. 269 (2015) 1899–1901] for higher dimensional case.

scholarly journals WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) TO BLOCH TYPE SPACES ON THE UNIT BALL

2008 ◽  
Vol 19 (08) ◽  
pp. 899-926 ◽  
Author(s):  
ZE-HUA ZHOU ◽  
REN-YU CHEN
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

scholarly journals Essential Norms of Weighted Composition Operators from theα-Bloch Space to a Weighted-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Lower And Upper Bounds ◽  
Type Space ◽  
Weighted Composition ◽  
Weighted Type

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator fromα-Bloch spaces to the weighted-type spaceHμ∞on the unit ball for the caseα≥1.

scholarly journals Weighted composition operators from weighted hardy spaces to weighted-type spaces

2013 ◽  
Vol 46 (2) ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Composition Operator ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Weighted Hardy Spaces ◽  
Type Spaces ◽  
Weighted Composition ◽  
Weighted Type

AbstractThe boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.

scholarly journals Weighted composition operators from Bloch-type into Bers-type spaces

2021 ◽  
Vol 29 (2) ◽  
pp. 243-250
Author(s):  
HAMID VAEZI ◽  
MOHAMAD NAGHLISAR
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Type Space ◽  
Bloch Type Space ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.

scholarly journals Spectrums and Uniform Mean Ergodicity of Weighted Composition Operators on Fock Spaces

2021 ◽  
Author(s):  
Werkaferahu Seyoum ◽  
Tesfa Mengestie
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Linear Expansion ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Fock Spaces ◽  
Ergodic Properties ◽  
Weighted Composition ◽  
Mean Ergodicity ◽  
Power Bounded

AbstractFor holomorphic pairs of symbols $$(u, \psi )$$ ( u , ψ ) , we study various structures of the weighted composition operator $$ W_{(u,\psi )} f= u \cdot f(\psi )$$ W ( u , ψ ) f = u · f ( ψ ) defined on the Fock spaces $$\mathcal {F}_p$$ F p . We have identified operators $$W_{(u,\psi )}$$ W ( u , ψ ) that have power-bounded and uniformly mean ergodic properties on the spaces. These properties are described in terms of easy to apply conditions relying on the values |u(0)| and $$|u(\frac{b}{1-a})|$$ | u ( b 1 - a ) | , where a and b are coefficients from linear expansion of the symbol $$\psi $$ ψ . The spectrum of the operators is also determined and applied further to prove results about uniform mean ergodicity.

Sign in / Sign up

Export Citation Format

Share Document