Growth of the Poisson-Stieltjes Integral in a Polydisc

Abstract

We describe the growth of the valueM∞(r1,..., rrn, v) = max{|v(z1,...,zn)| : |zj| ≤ rj}, 0 ≤ rj < 1 in terms of the modulus of continuity of a measure μ, where the function v is represented by the Poisson-Stieltjes integral.