两类双全纯映照子族在Roper-Suffridge延拓算子下的不变性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 209-219.

• 论文 • 下一篇

两类双全纯映照子族在Roper-Suffridge延拓算子下的不变性

王朝君¹(),崔艳艳¹,刘浩²()

¹ 周口师范学院数学与统计学院河南周口 466001
² 河南大学现代数学研究所河南开封 475001

收稿日期:2017-10-24 出版日期:2019-04-26 发布日期:2019-05-05
作者简介:王朝君, E-mail: wang9907081@163.com|刘浩, E-mail: haoliu@henu.edu.cn
基金资助:
国家自然科学基金(11271359);国家自然科学基金(11471098);河南省教育厅科学技术研究重点项目(17A110041);河南省教育厅科学技术研究重点项目(19B110016);周口师范学院科研创新基金项目(ZKNUA201805)

The Invariance of Two Subclasses of Biholomorphic Mappings Under the Roper-Suffridge Extension Operators

Chaojun Wang¹(),Yanyan Cui¹,Hao Liu²()

¹ College of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466001
² Institute of Contemporary Mathematics, Henan University, Henan Kaifeng 475001

Received:2017-10-24 Online:2019-04-26 Published:2019-05-05
Supported by:
the NSFC(11271359);the NSFC(11471098);the Science and Technology Research Projects of Henan Provincial Education Department(17A110041);the Science and Technology Research Projects of Henan Provincial Education Department(19B110016);the Scientific Research and Innovation Fund Projects of Zhoukou Normal University(ZKNUA201805)

摘要/Abstract

摘要：

该文将已有的Roper-Suffridge延拓算子在Bergman-Hartogs域上进行了推广，应用α次β型螺形映照及复数λ阶殆星映照的几何性质及增长定理，讨论了推广后的Roper-Suffridge延拓算子在Bergman-Hartogs域上保持α次β型螺形性及复数λ阶殆星性，并得到一些特殊情况.所得结论为构造多复空间中的α次β型螺形映照及复数λ阶殆星映照提供了新的途径.

关键词: Roper-Suffridge算子, 双全纯映照, Bergman-Hartogs域

Abstract:

In this paper, we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Applying the geometric properties and the growth theorems of spirallike mappings of type β and order α as well as almost starlike mappings of complex order λ, we obtain that the generalized Roper-Suffridge operators preserve spirallikeness of type β and order α as well as almost starlikeness of complex order λ on Bergman-Hartogs domains which lead to some special cases. The conclusions provide new approaches to construct spirallike mappings of type β and order α and almost starlike mappings of complex order λ in several complex variables.

Key words: Roper-Suffridge operators, Biholomorphic mappings, Bergman-Hartogs domains

中图分类号:

O174.56

王朝君,崔艳艳,刘浩. 两类双全纯映照子族在Roper-Suffridge延拓算子下的不变性[J]. 数学物理学报, 2019, 39(2): 209-219.

Chaojun Wang,Yanyan Cui,Hao Liu. The Invariance of Two Subclasses of Biholomorphic Mappings Under the Roper-Suffridge Extension Operators[J]. Acta mathematica scientia,Series A, 2019, 39(2): 209-219.

参考文献 18

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两类双全纯映照子族在Roper-Suffridge延拓算子下的不变性

The Invariance of Two Subclasses of Biholomorphic Mappings Under the Roper-Suffridge Extension Operators

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