在一般加权Bergman空间上的广义Volterra型算子  

Generalized Volterra Type Operators on General Weighted Bergman Space

作　　者：罗庆仙 LUO Qingxian(College of Science, Guangdong Maoming Preschool Normal College, Maoming 525200, China)

机构地区：[1]广东茂名幼儿师范专科学校理学院,广东茂名525200

出　　处：《广东石油化工学院学报》2020年第4期70-73,76,共5页Journal of Guangdong University of Petrochemical Technology

基　　金：广东茂名幼儿专科学校“十三五”规划课题(2020GMYSKT02)。

摘　　要：Bergman空间上的算子理论是函数空间与算子理论的重要内容。利用Volterra算子、加权复合算子、微分算子之间的关系,用一种全新的方法简捷地刻画了一般加权Bergman空间上广义Volterra算子的有界性和紧性,拓展了相关的结论。文中的方法极大地简化了经典的证明,对相关算子的研究有一定的启发。Operator theory on Bergman spaces is an important part of the theory on function spaces.Using the relations among Volterra operators,weighted composition operators and differential operators,the boundedness and compactness of generalized Volterra operators between Bergman spaces induced regular weights are characterized in a new and much easier way.The method used here simplifies the classical proof and directs a new way to deal with the similar questions.

关 键 词：Volterra型算子 DIRICHLET空间 加权BERGMAN空间 加权复合算子 有界性 紧性 

分 类 号：O177.2[理学—数学]