Growth of the Poisson-Stieltjes integrals in a half-plane (in Ukrainian)

Let $u$ be a harmonic function represented by the Poisson-Stieltjes-type integral in the upper half-plane. We find necessary and sufficient conditions for the relationship $ M_infty(y, u):=sup_{xin mathbb{R}} |u(x+iy)|=O(y^{-alpha})$, $alpha>0$, $ydownarrow 0$.