单位球Hardy空间上加权复合算子的交换子

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1606-1615.

单位球Hardy空间上加权复合算子的交换子

徐宁¹(),周泽华^2,*(),丁颖¹

¹ 江苏海洋大学理学院江苏连云港 222005
² 天津大学数学学院天津 300072

收稿日期:2020-06-04 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 周泽华 E-mail:xuning@jou.edu.cn;gx899200@126.com
作者简介:徐宁, E-mail: xuning@jou.edu.cn
基金资助:
国家自然科学基金(11771323);江苏海洋大学博士科研启动金(KQ17006)

Commutators of Weighted Composition Operators on Hardy Space of the Unit Ball

Ning Xu¹(),Zehua Zhou^2,*(),Ying Ding¹

¹ School of Science, Jiangsu Ocean University, Jiangsu Lianyungang 222005
² Department of Mathematics, Tianjin University, Tianjin 300072

Received:2020-06-04 Online:2021-12-26 Published:2021-12-02
Contact: Zehua Zhou E-mail:xuning@jou.edu.cn;gx899200@126.com
Supported by:
the NSFC(11771323);the Doctoral Research Launch Fund of Jiangsu Ocean University(KQ17006)

摘要/Abstract

摘要：

该文研究了单位球Hardy空间上非自同构线性分式加权复合算子的交换子.首先给出加权复合算子的交换子公式.然后根据线性分式映射的三种类型刻画交换子的紧性.最后得到当线性分式映射为抛物型时，交换子是紧的.

关键词: Hardy空间, 加权复合算子, 交换子

Abstract:

In this paper, we study commutators of weighted composition operators with linear fractional non-automorphisms on Hardy space of the unit ball. First, we obtain the formula of commutators of weighted composition operators. Then, we characterize compactness of commutators according to two special situations of linear fractional maps. Finally, we obtain that commutators are compact when linear fractional maps are parabolic and commutators are not compact when linear fractional maps are hyperbolic.

Key words: Hardy spaces, Weighted composition operators, Commutators

中图分类号:

O177.2

徐宁,周泽华,丁颖. 单位球Hardy空间上加权复合算子的交换子[J]. 数学物理学报, 2021, 41(6): 1606-1615.

Ning Xu,Zehua Zhou,Ying Ding. Commutators of Weighted Composition Operators on Hardy Space of the Unit Ball[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1606-1615.

参考文献 12

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