On the Classification of Points of a Unit Circle for Subharmonic Functions of the Class $$\mathfrak{A}{\kern 1pt} \text{*}$$

Abstract

A class \(\mathfrak{A}{\kern 1pt} \text{*}\) consisting of subharmonic functions in the unit disk such that their superpositions with some families of linear fractional automorphisms of the disk form normal families is considered. A theorem stating that for any function of class \(\mathfrak{A}{\kern 1pt} \text{*}\) the set of points of the unit circle can be represented as a union of a set of Fatou points, a set of generalized Plesner points, and a set of measure zero is proved.