THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

doi:10.1007/s10473-019-0414-0

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 1103-1120.doi: 10.1007/s10473-019-0414-0

THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

崔艳艳¹, 刘浩²

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

收稿日期:2018-02-01 修回日期:2018-08-06 出版日期:2019-08-25 发布日期:2019-09-12
通讯作者: Hao LIU E-mail:haoliu@henu.edu.cn
作者简介:Yanyan CUI,E-mail:cui9907081@163.com
基金资助:
This work is supported by NSF of China (11271359, 11471098), Science and Technology Research Projects of Henan Provincial Education Department (17A110041), Scientific Research and Innovation Fund Projects of Zhoukou Normal University (ZKNUA201805).

THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

Yanyan CUI¹, Hao LIU²

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

Received:2018-02-01 Revised:2018-08-06 Online:2019-08-25 Published:2019-09-12
Supported by:
This work is supported by NSF of China (11271359, 11471098), Science and Technology Research Projects of Henan Provincial Education Department (17A110041), Scientific Research and Innovation Fund Projects of Zhoukou Normal University (ZKNUA201805).

摘要/Abstract

摘要： We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bⁿ. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_Ω^*(β, A, B), strong and almost spirallike mappings of type β and order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

关键词: Biholomorphic mappings, spirallike mappings, Bergman-Hartogs domain, Roper-Suffridge operator

Abstract: We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bⁿ. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_Ω^*(β, A, B), strong and almost spirallike mappings of type β and order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

Key words: Biholomorphic mappings, spirallike mappings, Bergman-Hartogs domain, Roper-Suffridge operator

中图分类号:

32A30

崔艳艳, 刘浩. THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS[J]. 数学物理学报(英文版), 2019, 39(4): 1103-1120.

Yanyan CUI, Hao LIU. THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS[J]. Acta mathematica scientia,Series B, 2019, 39(4): 1103-1120.

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THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

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