Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains |
| |
Authors: | Roberto C Raimondo |
| |
Institution: | (1) University of Melbourne, 3010 Parkville, Victoria, Australia |
| |
Abstract: | In this paper we study the problem of the membership of H
ϕ 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 H
φ 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. |
| |
Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47B35 Secondary 47B38 |
本文献已被 SpringerLink 等数据库收录! |
|