Growth of the Poisson–Stieltjes integral in a polydisc

We describe the growth of the value $M_{\infty}(r_1,\dots,r_n,v)=\max\{|v\ (z_1,\dots,z_n)|:|z_j|\le r_j\}$, $0\le r_j<1$ in terms of the modulus of continuity of a measure $\mu$, where the function $v$ is represented by the Poisson–Stieltjes integral.