On some classes of harmonic functions with nonnegative harmonic majorants in the half-plane

Abstract

Some ω-weighted classes of harmonic functions are introduced in the upper half-plane, the representations of these classes are found. A description of the boundary values of the functions from the considered classes is given by means of a notion of ω-capacity on the real axis, which becomes an analog of Frostman’s α-capacity in a particular case.