Subclasses of Harmonic Functions with Nonnegative Harmonic Majorants in the Halfplane

In this chapter, we consider some \(\omega \) -weighted classes of harmonic functions possessing nonnegative harmonic majorants in the upper halfplane \(G^+\) . The descriptive representations for these classes are found. A description of the boundary values of the functions from the considered classes is given by means of the notion of \(\omega \) -capacity on the real axis, which becomes an analog of O. Frostman’s \(\alpha \) -capacity in a particular case.