关于加权复合算子在加权Dirichlet空间上的有界性  

On the Boundedness of Weighted Composition Operators on Weighted Dirichlet Spaces

作　　者：林庆泽[1] LIN Qingze(School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China)

机构地区：[1]广东工业大学应用数学学院,广州510520

出　　处：《应用泛函分析学报》2018年第4期369-376,共8页Acta Analysis Functionalis Applicata

摘　　要：设函数φ和Ф是复平面单位圆盘D上的解析函数且φ(D)D,则将加权复合算子定义为W_(φ,Ф):f→Фf°φ.当1<α+2<q≤p<∞时,本文给出了加权Dirichlet空间D_α~p中元素的基于有限零点的分解并得到了当φ是D上的共形满射时该加权复合算子W_(φ,Ф)从D_α~p到D_α~q的有界性的充要条件.最后,文章得到了当1 <α+2 <q,p <∞时乘法算子从D_α~p到D_α~q的有界性的充要条件.Let φ and φ be two analytic functions defined on the unit disk D such that φ(D)■D, then the weighted composition operator is the operator defined by Wφ,Ф: f→Фf°φ. When 1 <α+ 2<q≤p<∞,in this paper, we give the factorizations for the elements of the weighted Dirichlet space Dαp based on the zeros and obtain the necessary and sufficient conditions for the boundedness of Wφ,Ф from Dαp to Dαq when φ is a conformal mapping of D onto itself. Finally, we also obtain the necessary and sufficient conditions for the boundedness of multiplication operators from Dαp to Dαq when 1 <α+2<q,p<∞.

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

分 类 号：O177.2[理学—数学]