数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (6): 1835-1844.doi: 10.1016/S0252-9602(14)60127-2

• 论文 • 上一篇    下一篇

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

刘浩|夏红川*   

  1. Institute of Contemporary Mathematics, Henan University, Kaifeng 475001, China; School of Mathematical Science, Xiamen University, Xiamen 361005, China
  • 收稿日期:2013-05-28 修回日期:2014-05-15 出版日期:2014-11-20 发布日期:2014-11-20
  • 通讯作者: XIA Hong-Chuan,cuttheknots@126.com E-mail:haoliu@henu.edu.cn;cuttheknots@126.com
  • 基金资助:

    Supported by the NSFC (11271359).

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

 LIU Hao, XIA Hong-Chuan*   

  1. 夏红川|cuttheknots@126.com
  • Received:2013-05-28 Revised:2014-05-15 Online:2014-11-20 Published:2014-11-20
  • Supported by:

    Supported by the NSFC (11271359).

摘要:

In this paper, we construct a new Roper-Suffridge extension operator
Φrnβ1,… , βn(f)(z) = F(z) = ((rf( z1/r /z1 )β1 z1, (rf( z1/r /z1 )β2 z2, … , (rf( z1/r /z1 )βnzn)′,
where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z1| : z =(z1, … , zn) ∈Ω}, β1 ∈ [0, 1], 0≤ βk ≤ β1, k = 2, … , n, then we prove it can preserve the property of spirallikeness of type , almost starlikeness of order and starlikeness of order α on bounded complete Reinhardt domain Ω, respectively.

关键词: Roper-Suffridge operator, biholomorphic mappings, bounded complete Rein-hardt domains

Abstract:

In this paper, we construct a new Roper-Suffridge extension operator
Φrnβ1,… , βn(f)(z) = F(z) = ((rf( z1/r /z1 )β1 z1, (rf( z1/r /z1 )β2 z2, … , (rf( z1/r /z1 )βnzn)′,
where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z1| : z =(z1, … , zn) ∈Ω}, β1 ∈ [0, 1], 0≤ βk ≤ β1, k = 2, … , n, then we prove it can preserve the property of spirallikeness of type , almost starlikeness of order and starlikeness of order α on bounded complete Reinhardt domain Ω, respectively.

Key words: Roper-Suffridge operator, biholomorphic mappings, bounded complete Rein-hardt domains

中图分类号: 

  • 30C45