scholarly journals ORDER BOUNDED WEIGHTED COMPOSITION OPERATORS

2012 ◽  
Vol 93 (3) ◽  
pp. 333-343
Author(s):  
ELKE WOLF
Keyword(s):  
Composition Operators ◽  
Weighted Composition Operator ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Weighted Composition ◽  
Weighted Banach Spaces ◽  
Analytic Maps

AbstractLet $\phi $ and $\psi $ be analytic maps on the open unit disk $D$ such that $\phi (D) \subset D$. Such maps induce a weighted composition operator $C_{\phi ,\psi }$ acting on weighted Banach spaces of type $H^{\infty }$or on weighted Bergman spaces, respectively. We study when such operators are order bounded.

Closed range weighted composition operators on weighted Bergman spaces

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Elke Wolf
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Closed Range ◽  
Weighted Composition

AbstractLet ψ be an analytic map and ϕ an analytic self-map of the open unit disk

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.

scholarly journals DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS

2010 ◽  
Vol 52 (2) ◽  
pp. 325-332 ◽  
Author(s):  
ELKE WOLF
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Banach Spaces

AbstractWe characterise boundedness and compactness of differences of composition operators acting between weighted Bergman spaces Av, p and weighted Banach spaces H∞w of holomorphic functions defined on the open unit disk D.

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.

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