单位球上正规权Zygmund空间上的加权复合算子

摘要/Abstract

摘要：

设 $\mu$ 是 $[0, 1)$ 上的一个正规函数, $\varphi$ 是 ${\bf C}^{n}$ 中单位球 $B$ 上的一个全纯自映射, $\psi$ 是 $B$ 上的一个全纯函数.在本文中,作者刻画了 ${\bf C}^{n}$ 中单位球上具有正规权 $\mu$ 的Zygmund型空间 ${\cal Z}_{\mu}(B)$ 上加权复合算子 $\psi C_{\varphi}$ 的有界性和紧性.

关键词: 正规权Zygmund空间, 高维, 复合算子, 有界性, 紧性

Abstract:

Let $\mu$ be a normal function on $[0, 1)$ . Suppose that $\varphi$ is a holomorphic self-map on the unit ball $B$ in ${\bf C}^{n}$ and $\psi\in H(B)$ . Here the authors characterize the boundedness and compactness of the weighted composition operator $\psi C_{\varphi}$ on the Zygmund-type space ${\cal Z}_{\mu}(B)$ with a normal weight $\mu$ on the unit ball in ${\bf C}^{n}$ .

Key words: Normal weight Zygmund space, High dimensions, Composition operator, Boundedness, Compactness

中图分类号:

O174.56

徐思,张学军. 单位球上正规权Zygmund空间上的加权复合算子[J]. 数学物理学报, 2020, 40(2): 288-303.

Si Xu,Xuejun Zhang. Weighted Composition Operator on the Normal Weight Zygmund Space in the Unit Ball[J]. Acta mathematica scientia,Series A, 2020, 40(2): 288-303.

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