Hankel operators on standard Bergman spaces

We study Hankel operators on the standard Bergman spaces $A^{2}_{\alpha}, \alpha > -1$. A description of the boundedness and compactness of the (big) Hankel operator $H_f$ with general symbols $f \in L^2 (\mathbb{D}, d A_\alpha)$ is obtained. Also, we provide a new proof of a result of Arazy-Fish...

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Bibliographic Details
Author: Pau, Jordi
Format: article
Status:Versión aceptada para publicación
Publication Date:2013
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/96731
Online Access:https://hdl.handle.net/2445/96731
Access Level:Open access
Keyword:Funcions de variables complexes
Funcions analítiques
Operadors lineals
Nuclis de Bergman
Functions of complex variables
Analytic functions
Linear operators
Bergman kernel functions
Description
Summary:We study Hankel operators on the standard Bergman spaces $A^{2}_{\alpha}, \alpha > -1$. A description of the boundedness and compactness of the (big) Hankel operator $H_f$ with general symbols $f \in L^2 (\mathbb{D}, d A_\alpha)$ is obtained. Also, we provide a new proof of a result of Arazy-Fisher-Peetre on the membership in Schatten $p$-classes of Hankel operators with conjugate analytic symbols.