从混合模空间到Zygmund-型空间的一些积型算子

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 15-28.

从混合模空间到Zygmund-型空间的一些积型算子

刘永民¹(),于燕燕^2,*()

¹ 江苏师范大学数学与统计学院江苏徐州 221116
² 徐州工程学院数学与物理科学学院江苏徐州 221018

收稿日期:2017-10-25 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 于燕燕 E-mail:minliu@jsnu.edu.cn
作者简介:刘永民, E-mail:minliu@jsnu.edu.cn
基金资助:
国家自然科学基金(11771184);国家自然科学基金(11771188);江苏省基础研究计划(BK20161158)

On Some Product-Type Operators From Mixed Norm Space to Zygmund-Type Spaces

Yongmin Liu¹(),Yanyan Yu^2,*()

¹ School of Mathematics and Statistics, Jiangsu Normal University, Jiangsu Xuzhou 221116
² School of Mathematics and Physics Science, Xuzhou Institute of Technology, Jiangsu Xuzhou 221018

Received:2017-10-25 Online:2019-02-26 Published:2019-03-12
Contact: Yanyan Yu E-mail:minliu@jsnu.edu.cn
Supported by:
国家自然科学基金(11771184);国家自然科学基金(11771188);江苏省基础研究计划(BK20161158)

摘要/Abstract

摘要：

设${\mathbb D}=\{ z\in {\mathbb C}: |z|< 1 \}$是复平面上的单位圆盘, $H({\Bbb D})$表示${\Bbb D}$上的所有解析函数的集合, $\psi_1, \psi_2\in H({\Bbb D}),$ $n$是一个非负整数, $\varphi$是${\Bbb D}$到${\Bbb D}$的一个解析自映射, $\mu$是一个权函数.研究从混合模空间到Zygmund-型空间的积型算子$T^n_{\psi_{1},\psi_{2},\varphi}$的有界性和紧性特征,其中

$ T^n_{\psi_{1},\psi_{2},\varphi}f(z)=\psi_1(z)f^{(n)}(\varphi(z))+\psi_2(z)f^{(n+1)}(\varphi(z)), f\in H({\Bbb D}). $

关键词: 积型算子, 混合模空间, Zygmund-型空间, 克兰姆法则

Abstract:

Let $H({\Bbb D})$ denote the space of all analytic functions on the unit disk ${\Bbb D}$ in the complex plane $ {\Bbb C}$, $\psi_1, \psi_2\in H({\Bbb D}),$ $n$ be a nonnegative integer, $\varphi$ an analytic self-map of $ {\Bbb D}$ and $\mu$ a weight. We study the boundedness and compactness of a product-type operator which is defined by

$ T^n_{\psi_{1},\psi_{2},\varphi}f(z)=\psi_1(z)f^{(n)}(\varphi(z))+\psi_2(z)f^{(n+1)}(\varphi(z)), f\in H({\Bbb D}), $

from the mixed norm space to Zygmund-type spaces.

Key words: Product-type operator, Mixed norm space, Zygmund-type space, Cramer's Rule

中图分类号:

O177.2

刘永民,于燕燕. 从混合模空间到Zygmund-型空间的一些积型算子[J]. 数学物理学报, 2019, 39(1): 15-28.

Yongmin Liu,Yanyan Yu. On Some Product-Type Operators From Mixed Norm Space to Zygmund-Type Spaces[J]. Acta mathematica scientia,Series A, 2019, 39(1): 15-28.

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[1]	于燕燕, 刘永民. 从混合模空间到Bloch -型空间微分算子与乘子的积[J]. 数学物理学报, 2015, 35(2): 68-79.
[2]	刘永民, 于燕燕. 关于从混合模空间到小 \|Zygmund 空间的 Volterra 型复合算子[J]. 数学物理学报, 2015, 35(1): 210-217.
[3]	于燕燕, 刘永民. 从混合模空间到 Bloch -型空间微分算子与乘子的积[J]. 数学物理学报, 2012, 32(1): 68-79.