The Essential Norm of Hankel Operators on the Weighted Bergman Spaces with Exponential Type Weights

2006 ◽  
Vol 55 (1) ◽  
pp. 1-18 ◽  
Author(s):  
S. Asserda
Keyword(s):  
Exponential Type ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Hankel Operators ◽  
Weighted Bergman Spaces

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.

Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2

1998 ◽  
Vol 50 (3) ◽  
pp. 658-672 ◽  
Author(s):  
Frédéric Symesak
Keyword(s):  
Hardy Space ◽  
Finite Type ◽  
Pseudoconvex Domain ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Sufficient Condition ◽  
Schatten Class ◽  
Strictly Pseudoconvex Domain

AbstractThe aimof this paper is to study small Hankel operators h on the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2 or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbol ƒ so that h belongs to the Schatten class Sp, 1 ≤ p < +∞.

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 Hankel Operators on the WeightedLP-Bergman Spaces with Exponential Type Weights

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hong Rae Cho ◽  
Jeong Wan Seo
Keyword(s):  
Exponential Type ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Hankel Operators

We characterize the boundedness and compactness of the Hankel operator with conjugate analytic symbols on the weightedLP-Bergman spaces with exponential type weights.

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.

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