Integrals of differences of subharmonic functions. II. A criterion

TL;DR

This paper develops a new criterion based on measure and potential estimates for integrals of differences of subharmonic functions, extending to meromorphic functions on the complex plane.

Contribution

It introduces a novel criterion formulated solely in terms of measure and potential, with estimates for integrals of subharmonic function differences.

Findings

Provides integral estimates with measure and potential

Formulates a new criterion for subharmonic functions

Extends results to meromorphic functions

Abstract

We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a criterion, which is formulated exclusively in terms of the measure and its potential. This criterion is also new for meromorphic functions on the complex plane.