单位球上正规权Dirichlet型空间上的一种积分算子  

A Kind of Integral Operator on Normal Weight Dirichlet Type Space in the Unit Ball

作　　者：郭雨婷 张学军 GUO Yuting;ZHANG Xuejun(College of Mathematics and Statistics,Hunan Normal University,Changsha 410006,China.)

机构地区：[1]湖南师范大学数学与统计学院,长沙410006

出　　处：《数学年刊（A辑）》2023年第3期255-266,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11942109);湖南省自然科学基金资助(No.2022JJ30369)的资助。

摘　　要：设μ是[0,1)上的正规函数,Bn是n维复空间Cn上的单位球,ψ是Bn上的一个全纯函数,φ是Bn上的全纯自映射.作者考虑如下一种积分算子:Tφ,ψ(f)(z)=∫01f[φ(tz)]Rψ(tz)dt/t,z∈Bn.作者主要刻画了正规权Dirichlet型空间Dμp(Bn)(00)的同样问题.对讨论的情形本文均给出了充要条件.Letμbe a normal function on[0,1)and Bn be the unit ball in n dimensions complex space Cn.Suppose that b is a holomorphic function on Bn and p is a holomorphic self-map of Bn.The authors consider a kind of integral operator as follows:Tφ,ψ(f)(z)=∫01f[φ(tz)]Rψ(tz)dt/t,z∈Bn,The authors mainly characterize the boundedness and compactness of Te,b on the normal weight Dirichlet type space Dp(Bn)(0<p≤1).At the same time,the authors discuss the same problem from the normal weight Bergman space Ap(Bn)to Dp(Bn)(p>0)by measures on Carleson square and Bergman ball.Necessary and sufficient conditions are given for all the cases discussed.

关 键 词：复合Cesàro算子 Bergman型空间 DIRICHLET型空间 有界性 紧性 

分 类 号：O174.56[理学—数学]