On Decomposition Theorem of normalized biholomorphic convex mappings in Reinhardt domains

The construction of normalized biholomorphic convex mappings in the Reinhardt domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$D_p = \{ (z_1 ,z_2 , \cdots ,z_n ) \in \mathbb{C}^n :\left| {z_1 } \right|^{p_1 } + \left| {z_2 } \right|^{p_2 } + \cdots + \left| {z_n } \right|^{p_n } < 1\} $$ \end{document}, pj > 2, j = 1,2,⋯, n) of ℂn is discussed. The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each such mapping f, the first k-terms of the homogeneous expansion of its j-th component fj, j = 1, 2, ⋯, n, depends only on zj, where k is the number that satisfies k < min {p1, p2,⋯, pn ≤ k + 1. When p1,p2, ... ,pn → ∞ , this derives the Decomposition Theorem of normalized biholomorphic convex mappings in the polydisc which was gotten by T.J. Suffridge in 1970.