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Science in China Series A: Mathematics

, Volume 40, Issue 8, pp 799–806 | Cite as

Homogeneous expansions of normalized biholomorphic convex mappings overB P

  • Taishun Liu
  • Wenjun Zhang
Article

Abstract

The power series expansions of normalized biholomorphic convex mappings on the Reinhardt domain\(B^p = \left\{ z \right. \in \mathbb{C}^n :\left\| { z } \right\| _p = [\mathop \sum \limits_{j = 1} \left| {Z_j } \right| ^p ]^{1/p}< 1\} (p > 2 )\) are studied. It is proved that the first (k+1) terms of the expansions of the jth componentf j of such a mapf depend only onz j , for 1 ⩽j⩽n, wherek is the natural number that satisfiesk < ρ ⩽k +I. Whenp→ ∞, this gives the result on the unit polydisc obtained by Suffridge in 1970.

Keywords

biholomorphic convex mappings Reinhardt domains Schwarz-type lemma 

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Copyright information

© Science in China Press 1997

Authors and Affiliations

  • Taishun Liu
    • 1
  • Wenjun Zhang
    • 2
  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of MathematicsShenzhen UniversityShenzhenChina

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