Frequently oscillating families related to subharmonic functions

TL;DR

This paper extends bounds on the growth of frequently oscillating subharmonic functions to a broader class, refining techniques from Jones and Makarov to enhance understanding of harmonic measure properties.

Contribution

It introduces an extension of growth bounds for oscillating subharmonic functions and refines existing techniques for broader applicability.

Findings

Extended growth bounds to larger classes of functions.

Refined techniques from Jones and Makarov.

Improved understanding of harmonic measure properties.

Abstract

The goal of this note is to extend the result bounding from bellow the minimal possible growth of frequently oscillating subharmonic functions to a larger class of functions that carry similar properties. We refine and find further applications for the technique presented by Jones and Makarov in their celebrated paper, Density properties of harmonic measure.