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

doi:10.1016/S0252-9602(14)60127-2

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

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

刘浩|夏红川*

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*

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/Abstract

摘要：

In this paper, we construct a new Roper-Suffridge extension operator
Φ^r_n, β₁,… , β_n(f)(z) = F(z) = ((rf( z₁/r /z₁ )^β₁z₁, (rf( z₁/r /z₁ )^β₂z₂, … , (rf( z₁/r /z₁ )^β_nz_n)′,
where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z₁| : z =(z₁, … , z_n) ∈Ω}, β₁ ∈ [0, 1], 0≤ β_k ≤ 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:

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

中图分类号:

30C45

刘浩, 夏红川. A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS[J]. 数学物理学报(英文版), 2014, 34(6): 1835-1844.

LIU Hao, XIA Hong-Chuan. A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS[J]. Acta mathematica scientia,Series B, 2014, 34(6): 1835-1844.

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

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

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