scholarly journals Weighted Bergman spaces induced by doubling weights in the unit ball of $$\mathbb {C}^n$$

2020 ◽  
Vol 10 (4) ◽  
Author(s):  
Juntao Du ◽  
Songxiao Li ◽  
Xiaosong Liu ◽  
Yecheng Shi
Keyword(s):  
Unit Ball ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Doubling Weights

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.

Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball

2013 ◽  
Vol 78 (2) ◽  
pp. 271-300 ◽  
Author(s):  
Wolfram Bauer ◽  
Crispin Herrera Yañez ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Radial Operators

scholarly journals Composition Semigroups on Weighted Bergman Spaces Induced by Doubling Weights

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Fanglei Wu
Keyword(s):  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Resolvent Operators ◽  
Infinitesimal Generators ◽  
Compact Resolvent ◽  
Doubling Weights

We prove that composition semigroups are strongly continuous on weighted Bergman spaces with doubling weights. Point spectra and compact resolvent operators of infinitesimal generators of composition semigroups are characterized.

Pluriharmonic Symbols of Commuting Toeplitz Type Operators on the Weighted Bergman Spaces

1998 ◽  
Vol 41 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Young Joo Lee
Keyword(s):  
Unit Ball ◽  
Complex Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces

AbstractA class of Toeplitz type operators acting on the weighted Bergman spaces of the unit ball in the n-dimensional complex space is considered and two pluriharmonic symbols of commuting Toeplitz type operators are completely characterized.

BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL

2015 ◽  
Vol 99 (2) ◽  
pp. 237-249
Author(s):  
MAŁGORZATA MICHALSKA ◽  
PAWEŁ SOBOLEWSKI
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Necessary Condition ◽  
Sufficient Condition

Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.

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.

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