# The variation of the maximal function of a radial function

## TL;DR

This paper investigates how the variation of the Hardy-Littlewood maximal function behaves for radial functions in higher dimensions, establishing that their variations are comparable.

## Contribution

It proves that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the original function, extending understanding in higher dimensions.

## Key findings

- Variation of the maximal function is comparable to the original function's variation.
- Results apply to non-centered Hardy-Littlewood maximal functions.
- Focus on radial functions in higher dimensions.

## Abstract

We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the function itself.