Oscillation of H\"older Continuous Functions

TL;DR

This paper investigates the local oscillation of H"older continuous functions and demonstrates that their growth behavior follows a pattern similar to the Law of the Iterated Logarithm, revealing new insights into their fluctuation properties.

Contribution

It establishes a novel connection between the oscillation of H"older functions and probabilistic growth laws, extending classical results to a broader function class.

Findings

Oscillation growth is governed by a Law of the Iterated Logarithm variant.

Provides a new probabilistic characterization of H"older continuous functions.

Enhances understanding of the fluctuation behavior of functions satisfying H"older conditions.

Abstract

Local oscillation of a function satisfying a H\"older condition is considered and it is proved that its growth is governed by a version of the Law of the Iterated Logarithm.