Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (6): 1835-1844.doi: 10.1016/S0252-9602(14)60127-2

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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).

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

CLC Number: 

  • 30C45
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