Chordal and Angular Limits of Subordinate Subharmonic and Harmonic Functions

Abstract

In this article we consider classes of harmonic and subharmonic functions introduced with using integral operators Riman-Liouville by Professor M. Djrbashyan when α > 0. These classes are significant generalizations of already well known classes of harmonic and subharmonic functions match up with them only in a particular case. In our article we consider angular and chordal limits of harmonic and subharmonic functions got by using Riman-Liouville integral operators. A set of the points at which, probably, these limits don’t exist are characterized by using a linear measure of zero.