Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains
Authors:
Roberto C. Raimondo
Affiliation:
(1) University of Melbourne, 3010 Parkville, Victoria, Australia
Abstract:
In this paper we study the problem of the membership of Hϕ in the Hilbert-Schmidt class, when 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 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 with φ holomorphic.