数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1767-1779.doi: 10.1016/S0252-9602(16)30104-7

• 论文 • 上一篇    下一篇

PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

王朝君1, 崔艳艳1, 刘浩2   

  1. 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2. College of Mathematics and Statistics, Henan University, Kaifeng 475001, China
  • 收稿日期:2015-05-08 修回日期:2016-04-06 出版日期:2016-12-25 发布日期:2016-12-25
  • 通讯作者: Hao LIU,E-mail:haoliu@henu.edu.cn E-mail:haoliu@henu.edu.cn
  • 作者简介:Chaojun WANG,E-mail:wang9907081@163.com;Yanyan CUI,E-mail:cui9907081@163.com
  • 基金资助:

    This work was supported by NSFC (11271359, U1204618), Science and Technology Research Projects of Henan Provincial Education Department (14B110015, 14B110016), Youth Fund Projects of Zhoukou Normal University (zknuB3201608).

PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

Chaojun WANG1, Yanyan CUI1, Hao LIU2   

  1. 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2. College of Mathematics and Statistics, Henan University, Kaifeng 475001, China
  • Received:2015-05-08 Revised:2016-04-06 Online:2016-12-25 Published:2016-12-25
  • Contact: Hao LIU,E-mail:haoliu@henu.edu.cn E-mail:haoliu@henu.edu.cn
  • Supported by:

    This work was supported by NSFC (11271359, U1204618), Science and Technology Research Projects of Henan Provincial Education Department (14B110015, 14B110016), Youth Fund Projects of Zhoukou Normal University (zknuB3201608).

摘要:

In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ*(β, A, B), almost starlike mapping of complex order λ on Ωn,p2,…,pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order α, strongly pirallikeness of type β and order α, almost starlikeness of order α on Ωn,p2,…,pn. The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.

关键词: Roper-Suffridge operator, spirallike mappings, starlike mappings

Abstract:

In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ*(β, A, B), almost starlike mapping of complex order λ on Ωn,p2,…,pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order α, strongly pirallikeness of type β and order α, almost starlikeness of order α on Ωn,p2,…,pn. The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.

Key words: Roper-Suffridge operator, spirallike mappings, starlike mappings

中图分类号: 

  • 32A30