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

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.