The Best constant for the almost uncentered maximal operator on radial decreasing functions

TL;DR

This paper determines the minimal weak type (1,1) bound for the almost uncentered maximal operator when applied to radial decreasing functions, advancing understanding of maximal operators in harmonic analysis.

Contribution

It identifies the best constant for the almost uncentered maximal operator on radial decreasing functions, a specific case not previously characterized.

Findings

Established the least weak type (1,1) bound for the operator.

Provided explicit constant value for the maximal operator.

Enhanced understanding of maximal operators on radial decreasing functions.

Abstract

The purpose of this note is to find the least weak type $(1,1)$ bound for the almost uncentered maximal operator on radial decreasing functions.