Radial oscillation of harmonic functions in the Korenblum class

TL;DR

This paper investigates the radial behavior of harmonic functions within the Korenblum class in the unit disk, revealing that such functions either oscillate or grow slowly along most radii, depending on their estimates.

Contribution

It establishes a dichotomy in the radial behavior of harmonic functions in the Korenblum class based on their estimates, advancing understanding of their oscillation and growth patterns.

Findings

Functions with two-sided Korenblum estimates oscillate or grow slowly along most radii.

Almost all radii exhibit either oscillation or slow growth for these functions.

The results clarify the radial dynamics of harmonic functions in the Korenblum class.

Abstract

We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class. We prove that functions which admit two-sided Korenblum estimate either oscillate or have slow growth along almost all radii.