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 Isometric multiplication operators and weighted composition operators of BMOA

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ligang Geng
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

AbstractLet u be an analytic function in the unit disk $\mathbb{D}$ D and φ be an analytic self-map of $\mathbb{D}$ D . We give characterizations of the symbols u and φ for which the multiplication operator $M_{u}$ M u and the weighted composition operator $M_{u,\varphi }$ M u , φ are isometries of BMOA.

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 On the Norm of Certain Weighted Composition Operators on the Hardy Space

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
M. Haji Shaabani ◽  
B. Khani Robati
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Special Case

We obtain a representation for the norm of certain compact weighted composition operator on the Hardy space , whenever and . We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on and . Moreover, we characterize the norm and essential norm of such operators in a special case.

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 Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces

2020 ◽  
Vol 40 (4) ◽  
pp. 495-507
Author(s):  
Ching-on Lo ◽  
Anthony Wai-keung Loh
Keyword(s):  
Hardy Space ◽  
Unit Disk ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Weighted Composition

Let \(u\) and \(\varphi\) be two analytic functions on the unit disk \(\mathbb{D}\) such that \(\varphi(\mathbb{D}) \subset \mathbb{D}\). A weighted composition operator \(uC_{\varphi}\) induced by \(u\) and \(\varphi\) is defined on \(H^2\), the Hardy space of \(\mathbb{D}\), by \(uC_{\varphi}f := u \cdot f \circ \varphi\) for every \(f\) in \(H^2\). We obtain sufficient conditions for Hilbert-Schmidtness of \(uC_{\varphi}\) on \(H^2\) in terms of function-theoretic properties of \(u\) and \(\varphi\). Moreover, we characterize Hilbert-Schmidt difference of two weighted composition operators on \(H^2\).

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 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 Hardy Spaces into Logarithmic Bloch Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Banach Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Weighted Composition

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk&#x1D53B;whose elementsfsatisfy the condition∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|=0.

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