scholarly journals Characterization of Schatten-class Hankel operators on weighted Bergman spaces

2016 ◽  
Vol 165 (14) ◽  
pp. 2771-2791 ◽  
Author(s):  
Jordi Pau
Keyword(s):  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Schatten Class

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 < +∞.

On Hankel Forms of Higher Weights: The Case of Hardy Spaces

2010 ◽  
Vol 62 (2) ◽  
pp. 439-455
Author(s):  
Marcus Sundhäll ◽  
Edgar Tchoundja
Keyword(s):  
Hardy Spaces ◽  
Besov Spaces ◽  
Carleson Measure ◽  
Bergman Spaces ◽  
One Dimension ◽  
Weighted Bergman Spaces ◽  
Schatten Class ◽  
Full Characterization ◽  
Higher Weights

AbstractIn this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by Sundh¨all for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.

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
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