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 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.

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 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 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 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 fromH∞to the Bloch Space on the Polydisc

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Songxiao Li ◽  
Stevo Stevic
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Bounded Holomorphic

LetDnbe the unit polydisc ofℂn,ϕ(z)=(ϕ1(z),…,ϕn(z))be a holomorphic self-map ofDn, andψ(z)a holomorphic function onDn. LetH(Dn)denote the space of all holomorphic functions with domainDn,H∞(Dn)the space of all bounded holomorphic functions onDn, andB(Dn)the Bloch space, that is,B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|+supz∈Dn∑k=1n|(∂f/∂zk)(z)|(1−|zk|2)<+∞}. We give necessary and sufficient conditions for the weighted composition operatorψCϕinduced byϕ(z)andψ(z)to be bounded and compact fromH∞(Dn)to the Bloch spaceB(Dn).

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 CONTINUITY OF WEIGHTED COMPOSITION OPERATORS BETWEEN WEIGHTED BLOCH TYPE SPACES

2008 ◽  
Vol 78 (1) ◽  
pp. 111-115
Author(s):  
ELKE WOLF
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Sufficient Condition ◽  
Type Spaces ◽  
Weighted Composition ◽  
Analytic Maps

AbstractLet ϕ:D→D and ψ:D→ℂ be analytic maps. These induce a weighted composition operator ψCϕ acting between weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition when such an operator is continuous.

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