An inequality type condition for quasinearly subharmonic functions and applications

TL;DR

This paper establishes a new inequality for quasinearly subharmonic functions, leading to improved conditions for the existence of subharmonic minorants and criteria for separate quasinearly subharmonicity, unifying several previous results.

Contribution

It introduces a generalized inequality for quasinearly subharmonic functions and applies it to enhance existing theorems on subharmonic minorants and separate quasinearly subharmonicity.

Findings

Derived a new inequality for quasinearly subharmonic functions.

Improved conditions for the existence of the largest subharmonic minorant.

Provided a sufficient condition for separate quasinearly subharmonicity.

Abstract

Generalizing older works of Domar and Armitage and Gardiner, we give an inequality for quasinearly subharmonic functions. As an application of this inequality, we improve Domar's, Rippon's and our previous results concerning the existence of the largest subharmonic minorant of a given function. Moreover, and as an another application, we give a sufficient condition for a separately quasinearly subharmonic function to be quasinearly subharmonic. Our result contains the previous results of Lelong, of Avanissian, of Arsove, of Armitage and Gardiner, and of ours.