THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

doi:10.1007/s10473-021-0512-7

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1606-1618.doi: 10.1007/s10473-021-0512-7

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

梁玉霞

School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

收稿日期:2020-01-09 修回日期:2021-04-21 出版日期:2021-10-25 发布日期:2021-10-21
作者简介:Yuxia LIANG,E-mail:liangyx1986@126.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11701422).

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

Yuxia LIANG

School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

Received:2020-01-09 Revised:2021-04-21 Online:2021-10-25 Published:2021-10-21
Supported by:
This work was supported by the National Natural Science Foundation of China (11701422).

摘要/Abstract

摘要： There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions. In this paper, we present an equivalent characterization for the boundedness of the product operator $C_\varphi D^m$ acting on Bloch-type spaces of slice regular functions. After that, an equivalent estimation for its essential norm is established, which can imply several existing results on holomorphic spaces.

关键词: essential norm, differentiation, composition operator, Bloch-type space, slice regular functions

Abstract: There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions. In this paper, we present an equivalent characterization for the boundedness of the product operator $C_\varphi D^m$ acting on Bloch-type spaces of slice regular functions. After that, an equivalent estimation for its essential norm is established, which can imply several existing results on holomorphic spaces.

Key words: essential norm, differentiation, composition operator, Bloch-type space, slice regular functions

中图分类号:

30D45

梁玉霞. THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS[J]. 数学物理学报(英文版), 2021, 41(5): 1606-1618.

Yuxia LIANG. THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS[J]. Acta mathematica scientia,Series B, 2021, 41(5): 1606-1618.

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THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

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