scholarly journals Essential norm of weighted composition operators from H∞ to the Zygmund space

2016 ◽  
Vol 09 (07) ◽  
pp. 5082-5092 ◽  
Author(s):  
Qinghua Hu ◽  
Xiangling Zhu
Keyword(s):  
Composition Operators ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition

scholarly journals Essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 681-691 ◽  
Author(s):  
Qinghua Hu ◽  
Songxiao Li
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition

In this paper, we give some estimates for the essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space.

Essential norm of weighted composition operators

Analysis ◽  
2018 ◽  
Vol 38 (3) ◽  
pp. 145-154
Author(s):  
Kuldip Raj ◽  
Charu Sharma
Keyword(s):  
Composition Operators ◽  
Essential Norm ◽  
Function Spaces ◽  
Weighted Composition Operators ◽  
Closed Range ◽  
Weighted Composition

Abstract In the present paper we characterize the compact, invertible, Fredholm and closed range weighted composition operators on Cesàro function spaces. We also make an effort to compute the essential norm of weighted composition operators.

Weighted composition operators on weighted Bergman spaces induced by doubling weights

2020 ◽  
Vol 126 (3) ◽  
pp. 519-539
Author(s):  
Juntao Du ◽  
Songxiao Li ◽  
Yecheng Shi
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Schatten Class ◽  
Doubling Weight ◽  
Doubling Weights ◽  
Type Spaces ◽  
Weighted Composition

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.

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.

Essential norm estimates of weighted composition operators between Bergman spaces on strongly pseudoconvex domains

2007 ◽  
Vol 142 (3) ◽  
pp. 525-533 ◽  
Author(s):  
ŽELJKO ČUČKOVIĆ ◽  
RUHAN ZHAO
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Pseudoconvex Domains ◽  
Weighted Composition Operators ◽  
Norm Estimates ◽  
Strongly Pseudoconvex Domains ◽  
Weighted Composition

AbstractWe give estimates of the essential norms of weighted composition operators acting between Bergman spaces on strongly pseudoconvex domains. We also characterize boundedness and compactness of these operators.

scholarly journals Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Composition Operator ◽  
Besov Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition ◽  
Special Case

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.

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