| 张学军,范海霞,席利华,李俊锋.$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子[J].数学年刊A辑,2014,35(6):741~756 |
| $\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子 |
| Characterizations and Differentiation Composition Operators of $\mu$-Bergman Space in $\mathbb{C}^n$ |
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| DOI： |
| 中文关键词: $\mu$-Bergman空间, 刻画, 微分复合算子, 有界性, 紧性 |
| 英文关键词:$\mu$-Bergman space, Characterization, Differentiation composition operator, Boundedness, Compactness |
| 基金项目:湖南省教育厅重点基金(No.10A074, No.12A206), 湖南省重点学科建设项目和湖南师范大学数学与计算机科学学院
高性能计算与随机信息处理省部共建教育部重点实验室 |
| Author Name | Affiliation | E-mail | | ZHANG Xuejun | College of Mathematics and Computer Science, Hunan Normal University, Changsha
410081, China. | xuejunttt@263.net | | FAN Haixia | College of Mathematics and Computer Science, Hunan Normal University, Changsha
410081, China. | | | XI Lihua | College of Mathematics and Computer Science, Hunan Normal University, Changsha
410081, China. | | | LI Junfeng | College of Mathematics and Computer Science, Hunan City University, Yiyang
413000, Hunan, China. | li_jfeng@sina.com |
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| 中文摘要: |
| 设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画;
然后
分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的
微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为
$A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件. |
| 英文摘要: |
| Let $p>0$, $\mu$ and $\mu_{1}$ be two normal functions on $[0,1)$. In
this paper, a kind of equivalent characterizations of the $\mu$-Bergman space on the unit ball in $\mathbb{C}^{n}$
are given first. Furthermore, the necessary and sufficient conditions that the differentiation composition operator
$D_{\varphi}$ is
a bounded operator or a compact operator from $A^{p}(\mu)$ to $A^{p}(\mu_{1})$ are given, respectively.
At the same time, a simple sufficient condition and
the necessary condition that $D_{\varphi}$ is
a compact operator from $A^{p}(\mu)$ to $A^{p}(\mu_{1})$ are given. |
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