Homogeneous expansions of normalized biholomorphic convex mappings overB
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| Authors: | Taishun Liu Wenjun Zhang |
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| Institution: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, China;(2) Department of Mathematics, Shenzhen University, 518060 Shenzhen, China |
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| Abstract: | The power series expansions of normalized biholomorphic convex mappings on the Reinhardt domain
![$$B^p = \left\{ z \right. \in \mathbb{C}^n :\left\| { z } \right\| _p = \mathop \sum \limits_{j = 1} \left| {Z_j } \right| ^p ]^{1/p}< 1\} (p > 2 )$$](/content/8872748j7m81l3x4/11425_2008_Article_BF02878918_TeX2GIFIE1.gif)
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.
Project supported in part by the National Natural Science Foundation of China. |
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| Keywords: | biholomorphic convex mappings Reinhardt domains Schwarz-type lemma |
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