单位球上加权Bergman空间到Ƶμ型空间的加权Cesàro算子

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 569-578.

单位球上加权Bergman空间到Ƶ_μ型空间的加权Cesàro算子

赵艳辉^1,*(),吴修云²,廖春艳¹

¹ 湖南科技学院理学院湖南永州 425199
² 安徽师范大学数学与统计学院安徽芜湖 241003

收稿日期:2018-10-23 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 赵艳辉 E-mail:1261450046@qq.com
基金资助:
湖南省自然科学基金(2019JJ40089);湖南省自然科学基金(2018JJ3192);湖南科技学院应用特色学科建设项目

Extended Cesàro Operator from Weighted Bergman Spaces to Ƶ_μ Type Spaces on the Unit Ball

Yanhui Zhao^1,*(),Xiuyun Wu²,Chunyan Liao¹

¹ College of Science, Hunan University of Science and Engineering, Hunan Yongzhou 425199
² School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241003

Received:2018-10-23 Online:2020-06-26 Published:2020-07-15
Contact: Yanhui Zhao E-mail:1261450046@qq.com
Supported by:
the NSF of Hunan Province(2019JJ40089);the NSF of Hunan Province(2018JJ3192);the Construct Program Applied Characteristic Discipline in Hunan University of Science and Engineering

摘要/Abstract

摘要：

该文利用泛函分析以及多复变的方法，研究了单位球B上加权Bergman空间到Ƶ_μ型空间的加权Cesàro算子的有界性和紧性问题.获得了单位球上加权Bergman空间到Ƶ_μ型空间的加权Cesàro算子为有界算子和紧算子的充要条件.

关键词: 加权Bergman空间, Ƶ_μ型空间, 加权Cesàro算子, 有界性, 紧性

Abstract:

Some questions of extended Cesàro operator from weighted Bergman space to Ƶμ type spaces in the unit ball were studied in this paper. By the methods of functional analysis and several complex variables, the necessary and sufficient conditions are given for extended Cesàro operator to be bounded and compact from weighted Bergman space to Ƶ_μ type spaces in the unit ball.

Key words: Weighted Bergman space, Ƶ_μ type spaces, Extended Cesàro operator, Bounded, Compact

中图分类号:

O174.56

赵艳辉,吴修云,廖春艳. 单位球上加权Bergman空间到Ƶ_μ型空间的加权Cesàro算子[J]. 数学物理学报, 2020, 40(3): 569-578.

Yanhui Zhao,Xiuyun Wu,Chunyan Liao. Extended Cesàro Operator from Weighted Bergman Spaces to Ƶ_μ Type Spaces on the Unit Ball[J]. Acta mathematica scientia,Series A, 2020, 40(3): 569-578.

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