Toeplitz Operators and Herz Spaces on the Half-Space |
| |
Authors: | Boo Rim Choe Kyesook Nam |
| |
Affiliation: | (1) Department of Mathematics, Korea University, Seoul, 136–701, Korea;(2) Department of Mathematics, Hanshin University, Gyeonggi, 447–791, Korea |
| |
Abstract: | On the setting of the half-space we introduce the Schatten-Herz classes of Toeplitz operators and obtain characterizations for positive Toeplitz operators to belong to those classes. We also prove results concerning the boundedness and compactness of Toeplitz operators with Herz symbols. Such a study has been recently done on the ball. At a critical step of the proofs we employ a much simplified argument to extend the range of parameters for Herz spaces on which the Berezin transform is bounded. Our results show not only that most of results on the ball continue to hold, but also that there is some pathology caused by the unboundedness of the domain. The first author was in part supported by a Korea University Grant(2007), the second author was in part supported by Hanshin University Research Grant, and both authors were in part supported by KOSEF(R01-2003-000-10243-0). |
| |
Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 47B35 Secondary 46E30 |
本文献已被 SpringerLink 等数据库收录! |
|