Abstract
1. Introduction. Let n be a positive integer. Write = Bn for the unit ball in Cn and let S = Sn = dBn. When n = 1, we use the notation U and T in place of B and S\, respectively. We shall let σ = σn denote the unique normalized rotation-invariant Borel measure on S and m the normalized area measure on C. The symbol Pn stands for the class of holomorphic homogeneous polynomials Λ on Cn normalized so that A(B) = U. The maximum modulus set Λ1 (T) n S of Λ e P n is denoted by MaxΛ. It is assumed n > 2 in the rest of the paper unless otherwise specified. To begin with, let us look at some special cases which motivated the main results of this paper. We have the following change-ofvariables formula for Λ e Pn of degree 1 [Ru, Section 1.4]:
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