scholarly journals Composition operators on weighted Bergman spaces of a half-plane

2011 ◽  
Vol 54 (2) ◽  
pp. 373-379 ◽  
Author(s):  
Sam J. Elliott ◽  
Andrew Wynn
Keyword(s):  
Spectral Radius ◽  
Half Plane ◽  
Composition Operator ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Angular Derivative ◽  
The Right

AbstractWe use induction and interpolation techniques to prove that a composition operator induced by a map ϕ is bounded on the weighted Bergman space $\mathcal{A}^2_\alpha(\mathbb{H})$ of the right half-plane if and only if ϕ fixes the point at ∞ non-tangentially and if it has a finite angular derivative λ there. We further prove that in this case the norm, the essential norm and the spectral radius of the operator are all equal and are given by λ(2+α)/2.

scholarly journals Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Stevo Stević ◽  
Ajay K. Sharma ◽  
S. D. Sharma
Keyword(s):  
Half Plane ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition ◽  
Upper Half Plane ◽  
Weighted Type

Letψbe a holomorphic mapping on the upper half-planeΠ+={z∈ℂ:Jz>0}andφbe a holomorphic self-map ofΠ+. We characterize bounded weighted composition operators acting from the weighted Bergman space to the weighted-type space on the upper half-plane. Under a mild condition onψ, we also characterize the compactness of these operators.

SPECTRA OF LINEAR FRACTIONAL COMPOSITION OPERATORS ON THE GROWTH SPACE AND BLOCH SPACE OF THE UPPER HALF-PLANE

2018 ◽  
Vol 107 (02) ◽  
pp. 199-214
Author(s):  
SHI-AN HAN ◽  
ZE-HUA ZHOU
Keyword(s):  
Spectral Radius ◽  
Half Plane ◽  
Composition Operator ◽  
Fractional Composition ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Essential Spectral Radius ◽  
Growth Space ◽  
Upper Half Plane

In this article, we provide a complete description of the spectra of linear fractional composition operators acting on the growth space and Bloch space over the upper half-plane. In addition, we also prove that the norm, essential norm, spectral radius and essential spectral radius of a composition operator acting on the growth space are all equal.

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

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 Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

2009 ◽  
Vol 7 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

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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