Domination conditions for families of quasinearly subharmonic functions

TL;DR

This paper extends Domar's and Rippon's results on conditions for the existence of the largest subharmonic minorant to the broader classes of subharmonic and quasinearly subharmonic functions, improving previous conditions.

Contribution

It introduces a generalized and flexible modification of Domar's original argument, applicable to quasinearly subharmonic functions, enhancing the theoretical framework.

Findings

Extended Domar's condition to quasinearly subharmonic functions

Provided a more general criterion for the existence of the largest minorant

Improved upon Rippon's results with a flexible approach

Abstract

Domar has given a condition that ensures the existence of the largest subharmonic minorant of a given function. Later Rippon pointed out that a modification of Domar's argument gives in fact a better result. Using our previous, rather general and flexible, modification of Domar's original argument, we extend their results both to the subharmonic and quasinearly subharmonic settings.