对数Bloch型空间上微分复合算子乘积的本性范数
Product of Differentiation and Composition Operators on the Logarithmic Bloch Type Space
周继振 1王青青1
作者信息
- 1. 安徽理工大学数学与大数据学院,安徽 淮南 232001
- 折叠
摘要
目的 为刻画微分复合算子乘积CφDm在对数Bloch型空间上的本性范数特征.方法 利用有界序列{zn}n=1刻画对数Bloch型空间上微分复合算子乘积CφDm的有界性特征,以及泛函分析中的算子理论,例如紧算子性质和对本性范数上下界的估计.结果 在CφDm有界的条件下,给出了微分复合算子CφDm的本性范数特征,即这里m为非负正整数,微分复合算子乘积为CφDmf=f(m)°φ.结论 在CφDm有界的条件下,则微分复合算子CφDm的本性范数可由有界序列{zn}n=1的特征刻画.
Abstract
Objective To characterize the boundedness and essential norms of the product of differentiation and composition operators CφDm on logarithmic Bloch type spaces.Methods A bounded sequence { zn } n=1 was used to characterize the boundedness of the product of differential composite operators CφDm on logarithmic Bloch type spaces and the operator theory in functional analysis,such as the properties of compact operators.Results The es-sential norm of the product of differentiation and composition operators CφDm on the logarithmic Bloch type was obtained.Here m is a nonnegative positive integer,and the product of the differentiation and composition operator CφDm is defined by CφDmf=f(m)°φ.Conclusion If the product of differential composite operators CφDm on logarith-mic Bloch type spaces is bounded,the essential norm of C Dm may be characterized by the characteristics of the bounded sequence { zn}.
关键词
对数a-Bloch空间/复合算子/微分算子/有界性/本性范数Key words
Logarithmic a-Bloch space/composition operators/differential operator/boundedness/essential norms引用本文复制引用
基金项目
国家自然科学基金资助项目(11801347)
出版年
2024
NETL
NSTL
万方数据