向量值指数权Bergman空间上的正算子值Toeplitz算子  

Positive Operator-valued Toeplitz Operators on Vector-valued Exponential Weighted Bergman Spaces

作　　者：许春续 何莉[1] Chun Xu XU;Li HE(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,P.R.China)

机构地区：[1]广州大学数学与信息科学学院,广州510006

出　　处：《数学学报（中文版）》2024年第5期807-829,共23页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12371127)。

摘　　要：本文介绍向量值指数权Bergman空间A_(φ)^(p)(H)(1φp(H)到A_(φ)^(p)(H)上的Bergman投影何时是有界的,得到了向量值指数权Bergman空间的对偶.其次,得到了Carleson条件的几种等价描述,并用之来刻画Toeplitz算子在A_(φ)^(p)(H)上的有界性和紧性.最后,考虑了作用于A_(φ)^(2)(H)上的Toeplitz算子的Schatten-p类.We study some properties of Toeplitz operators with positive operatorvalued function symbols on the vector-valued exponential weighted Bergman spaces A_(φ)^(p)(H)(1<p<∞).Firstly,we discuss when the Bergman projection from Lβ(H)onto A_(φ)^(p)(H)onto A_(φ)^(p)(H)is bounded and get the dual of the vector-valued exponential weighted Bergman spaces.Secondly,we obtain several equivalent descriptions of Carleson condition to characterize the boundedness and compactness of Toeplitz operators on A_(φ)^(p)(H).Finally,we consider the Schatten-p class membership of Toeplitz operators acting on A_(φ)^(2).

关 键 词：TOEPLITZ算子 指数权Bergman空间 算子值符号 Carleson条件 Schatten-p类 

分 类 号：O177[理学—数学]