HOMOGENEOUS EXPANSIONS OF NORMALIZED BIHOLOMORPHIC CONVEX MAPPINGS OVER B-P

The power series expansions of normalized biholomorphic convex mapping s on the Reinhardt domain B-p = {z is an element of C-n: parallel to z parallel to(p) = [Sigma(j = 1)\Z(j)\(p)](1/p) < 1} (p > 2) are studie d. It is proved that the first (k + 1) terms of the expansions of the jth component f(j) of such a map f depend only on z(j) for 1 less than or equal to j less than or equal to n, where k is the natural number that satisfies k < p less than or equal to k + 1. When p --> infinity, this gives the result on the unit polydisc obtained by Suffridge in 1 970.