On quasinearly subharmonic functions

TL;DR

This paper explores quasinearly subharmonic functions, highlighting their properties, including their relation to other function classes and the conditions under which their sum remains quasinearly subharmonic, as well as characterizing harmonicity.

Contribution

It provides a comprehensive overview of quasinearly subharmonic functions, including their inclusion relations, sum properties, and a characterization of harmonic functions within this class.

Findings

Sum of two quasinearly subharmonic functions may not be quasinearly subharmonic

Quasinearly subharmonic functions include subharmonic, quasisubharmonic, nearly subharmonic, and almost subharmonic functions

Harmonicity can be characterized via quasinearly subharmonicity

Abstract

We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic functions. It is shown that the sum of two quasinearly subharmonic functions may not be quasinearly subharmonic. Moreover, we characterize the harmonicity via quasinearly subharmonicity.