Positivity of Toeplitz Operators on Harmonic Bergman Space

作     者：Yong Lu SHU Xian Feng ZHAO 

作者机构：College of Mathematics and StatisticsChongqing University Shanghai Center for Mathematical SciencesFudan University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2016年第32卷第2期

页      面：175-186页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by NSFC(Grant No.11271387) Chongqing Natural Sience Foundation(Grant No.cstc2013jjB0050) 

主　　题：Positive Toeplitz operators harmonic Bergman space Berezin transform 

摘      要：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.