| 郭雨婷,张学军.单位球上正规权 Dirichlet型空间上的一种积分算子*[J].数学年刊A辑,2023,44(3):255~266 |
| 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 |
| Received:October 25, 2022 Revised:April 23, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0018 |
| 中文关键词: 复合 Ces\`{a}ro 算子, Bergman型空间, Dirichlet 型空间, 有界性, 紧性 |
| 英文关键词:Composition Ces`aro operator, Bergman type space, Dirichlet type space, Boundedness, Compactness |
| 基金项目:国家自然科学基金(No.11942109)和湖南省自然科学基金资助 (No.2022JJ30369) |
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| 中文摘要: |
| 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,? 是 Bn 上的全纯自映射. 作者考虑如下一种积分算子:T?,ψ(f)(z) =Z01f[?(tz)]Rψ(tz)dt/t, z ∈ Bn.作者主要刻画了正规权Dirichlet型空间Dpμ(Bnn) (0 < p ≤ 1) 上 T?,ψ 的有界性和紧性.同时, 本文利用Carleson 方块和Bergman球的测度讨论了正规权Bergman型空间Apμ(Bn) 到 Dpμ(Bn) (p > 0)的同样问题. 对讨论的情形本文均给出了充要条件. |
| 英文摘要: |
| Let μ be a normal function on [0, 1) and Bn be the unit ball in n dimensions complex space Cn. Suppose that ψ is a holomorphic function on Bn and ? is a holomorphic self-map of Bn. The authors consider a kind of integral operator as follows:T?,ψ(f)(z) =Z01f[?(tz)]Rψ(tz)dt/t, z ∈ Bn.The authors mainly characterize the boundedness and compactness of T?,ψ on the normal weight Dirichlet type space Dpμ(Bnn) (0 < p ≤ 1) At the same time, the authors discuss the same problem from the normal weight Bergman space Apμ(Bn) to Dpμ(Bn) (p > 0) by measures on Carleson square and Bergman ball. Necessary and sufficient conditions are given for all the cases discussed. |
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