带有调和符号的交换Toeplitz算子  

Commuting Toeplitz Operators with Harmonic Symbols

作　　者：赵振刚[1] Zhen Gang ZHAO(School of Mathematical Science,Capital Normal University,Beijing 100048,P.R.China)

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《数学学报（中文版）》2023年第3期495-508,共14页Acta Mathematica Sinica：Chinese Series

摘　　要：我们研究作用于调和Bergman空间b^(2)(D{0})上的带有调和符号的Toeplitz算子,其中D是复平面上的单位圆盘.首先,研究b^(p)(Ω)的结构并且获得b^(p)(Ω)中的每个元在调和Bergman投影之下的像.其次,证明特殊的Toeplitz算子Tlog|w|:b^(2)(D{0})→b^(2)(D/{0})是有界线性算子并获得带有调和或全纯符号的Toeplitz算子与T_(log|w|)可交换的充分必要条件.第三,我们获得两个带有全纯符号的Toeplitz算子可交换的充分必要条件.第四,给出带有全纯符号的正规Toeplitz算子的一个特征.最后,得到带有调和符号的Toeplitz算子彼此之间可交换的一个必要条件.We investigate Toeplitz operators with harmonic symbols acting on the harmonic Bergman space for the punctured domain D\{O},where D is the unit disc in the complex plane.First,we investigate the construction of b^(p)(Ω)and derive the image of every element of b^(p)(Ω)under the harmonic Bergman projection.Second,we prove that the special Toeplitz operator Tlog|w|:b^(2)(D{0})→b^(2)(D/{0})is a bounded linear operator and obtain some sufficient and necessary conditions that a Toeplitz operator with harmonic or holomorphic symbol can commute with Tiog lwl-Third,We obtain a sufficient and necessary condition for two Toeplitz operators with holomorphic symbols commuting with each other.Fourth,we give a characterization of normal Toeplitz operators with holomorphic symbols.Finally,we derive a necessary condition for Toeplitz operators with harmonic symbols commuting with each other.

关 键 词：调和Bergman空间 TOEPLITZ算子 BERGMAN核 

分 类 号：O174.3[理学—数学]