Sharp constants in the classical weak form of the John--Nirenberg inequality

TL;DR

This paper determines the exact sharp constants in the classical weak form of the John--Nirenberg inequality using a Bellman function approach, providing precise bounds for the inequality.

Contribution

It introduces a Bellman function method to explicitly compute the sharp constants in the weak John--Nirenberg inequality, advancing the understanding of these bounds.

Findings

Exact sharp constants are derived for the weak John--Nirenberg inequality.

The Bellman function approach effectively computes these optimal constants.

Results improve the precision of bounds in the classical inequality.

Abstract

The sharp constants in the classical John--Nirenberg inequality are found by using Bellman function approach.