Positivity of Toeplitz operators on harmonic Bergman space |
| |
Authors: | Yong Lu Shu Xian Feng Zhao |
| |
Affiliation: | 1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China and Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China |
| |
Abstract: | In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator. |
| |
Keywords: | Positive Toeplitz operators harmonic Bergman space Berezin transform |
本文献已被 CNKI SpringerLink 等数据库收录! |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
|
点击此处可从《数学学报(英文版)》下载免费的PDF全文 |