单位球上加权Bergman空间到Zμ型空间的加权Cesàro算子  

Extended Cesaro Operator from Weighted Bergman Spaces to Zμ Type Spaces on the Unit Ball

作　　者：赵艳辉 吴修云 廖春艳 Zhao Yanhui;Wu Xiuyun;Liao Chunyan(College of Science,Hunan University of Science and Engineering,Hunan Yongzhou 425199;School of Mathematics and Statistics,Anhui Normal University,Anhui Wuhu 241003)

机构地区：[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

出　　处：《数学物理学报（A辑）》2020年第3期569-578,共10页Acta Mathematica Scientia

基　　金：湖南省自然科学基金(2019JJ40089,2018JJ3192);湖南科技学院应用特色学科建设项目。

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Zμ型空间的加权Cesaro算子的有界性和紧性问题.获得了单位球上加权Bergman空间到Zμ型空间的加权Cesaro算子为有界算子和紧算子的充要条件.Some questions of extended Cesàro operator from weighted Bergman space to Zμtype 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 Cesaro operator to be bounded and compact from weighted Bergman space to Zμtype spaces in the unit ball.

关 键 词：加权BERGMAN空间 Zμ型空间 加权CESÀRO算子 有界性 紧性 

分 类 号：O174.56[理学—数学] O177.2[理学—基础数学]