Radial growth of functions from the Korenblum space

TL;DR

This paper investigates the radial growth and decay patterns of analytic and harmonic functions in the Korenblum space, showing that extremal behaviors are confined to small sets of radii with precise estimates.

Contribution

It provides new insights into the radial behavior of functions in the Korenblum space, including bounds on exceptional sets where extremal growth or decay occurs.

Findings

Extremal growth or decay occurs only along small sets of radii.

Precise estimates of the size of these exceptional sets.

Radial behavior is tightly controlled by the majorant conditions.

Abstract

We study radial behavior of analytic and harmonic functions, which admit a certain majorant in the unit disk. We prove that extremal growth or decay may occur only along small sets of radii and give precise estimates of these exceptional sets.