从Zygmund型空间到空间的加权复合算子

郭洁婷，谭海鸥



郭洁婷，谭海鸥

（五邑大学 数学与计算科学学院，广东 江门 529020）

令,分别是复平面上的单位开圆盘中的解析自映射和解析函数. 加权复合算子定义为，，讨论了该加权复合算子从Zygmund型空间到-Bloch空间的有界性.

加权复合算子；-Bloch空间；Zygmund型空间；有界性

1 预备知识

Bloch型空间到其他全纯函数空间的复合算子与加权复合算子的研究成果详见文献[5-12]，关于Zygmund空间上的复合算子的有界性的一些特征见文献[13-15]. 本文主要研究从Zygmund型空间到空间的加权复合算子的有界性，可看作是对文献[16-17]中结果的推广.

2 主要结果

首先给出有用的引理.

引理1[18]若，则

由式（6）和式（10），有：

由式（8）、式（11）和式（12），得证.

由式（8）、式（14）和式（15），得证.

由式（6）、式（8）、式（17）和式（18），得证.

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[责任编辑：熊玉涛]

Weighted Composition Operators from Zygmund Type Spaces intoSpaces

GUOJie-ting, TANHai-ou

(School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China)

Letbe an analytic self-map andbe a fixed analytic function in the open unit diskon the complex plane. The weighted composition operator is defined by,. This paper studies the boundedness of the weighted composition operators from Zygmund type spaces to-Bloch spaces.

weighted composition operators;-Bloch spaces; Zygmund type space; boundedness

1006-7302（2015）02-0006-06

O174.5

A

2014-12-03

郭洁婷（1989—），女，广东鹤山人，在读硕士生，研究方向为复分析；谭海鸥，教授，硕士，硕士生导师，通信作者，研究方向为复分析.