Products of Volterra type operators and composition operators between weighted Bergman spaces of infinite order and weighted Bloch type spaces

2010 ◽  
Vol 17 (3) ◽  
pp. 621-627 ◽  
Author(s):  
Elke Wolf
Keyword(s):  
Infinite Order ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Volterra Type ◽  
Volterra Operators ◽  
Type Spaces

Abstract We study the boundedness and compactness of products of Volterra operators and composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces Bw .

scholarly journals Weighted composition operators with closed range

2007 ◽  
Vol 75 (3) ◽  
pp. 331-354 ◽  
Author(s):  
N. Palmberg
Keyword(s):  
Infinite Order ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Closed Range ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

We study the closed range property of weighted composition operators on weighted Bergman spaces of infinite order (including the Hardy space of infinite order). We give some necessary and sufficient conditions and find a complete characterisation for weighted composition operators associated with conformal mappings. We also give the corresponding results for composition operators on the Bloch-type spaces. Therefore, the results obtained in this paper also improve and generalise the results of Ghatage, Yan, Zheng and Zorboska.

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 Essential Norm of Difference of Composition Operators from Weighted Bergman Spaces to Bloch-Type Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ram Krishan ◽  
Mehak Sharma ◽  
Ajay K. Sharma
Keyword(s):  
Lower Bounds ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Upper And Lower Bounds ◽  
Weighted Bergman Spaces ◽  
Type Spaces ◽  
Difference Of Composition Operators

We compute upper and lower bounds for essential norm of difference of composition operators acting from weighted Bergman spaces to Bloch-type spaces.

scholarly journals COMPACT DIFFERENCES OF COMPOSITION OPERATORS

2008 ◽  
Vol 77 (1) ◽  
pp. 161-165 ◽  
Author(s):  
ELKE WOLF
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Infinite Order ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Difference

AbstractLet ϕ and ψ be analytic self-maps of the open unit disk. Each of them induces a composition operator, Cϕ and Cψ respectively, acting between weighted Bergman spaces of infinite order. We show that the difference Cϕ−Cψ is compact if and only if both operators are compact or both operators are not compact and the pseudohyperbolic distance of the functions ϕ and ψ tends to zero if ∣ϕ(z)∣→1 or ∣ψ(z)∣→1.

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