In this paper we study the problem of the membership of H ∅ in the Hilbert-Schmidt class, when ∅ ∈ L ∞ (Ω) and Ω is a planar domain. We find a necessary and sufficient condition. We apply this result to the problem of joint membership of Hφ and Hφ̄ in the Hilbert-Schmidt class. Using the notion of Berezin Transform and a result of K. Zhu we are able to give a necessary and sufficient condition. Finally, we recover a result of Arazy, Fisher and Peetre on the case Hφ̄ with φ holomorphic. © 2006 Birkhäuser Verlag Basel/Switzerland.
Raimondo, R. (2007). Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains. INTEGRAL EQUATIONS AND OPERATOR THEORY, 57, 425-449.
Citazione: | Raimondo, R. (2007). Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains. INTEGRAL EQUATIONS AND OPERATOR THEORY, 57, 425-449. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains |
Autori: | Raimondo, R |
Autori: | |
Data di pubblicazione: | 2007 |
Lingua: | English |
Rivista: | INTEGRAL EQUATIONS AND OPERATOR THEORY |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00020-006-1460-2 |
Appare nelle tipologie: | 01 - Articolo su rivista |