# A sharp symmetric integral form of the John-Nirenberg inequality

## TL;DR

This paper establishes sharp constants for a symmetric integral form of the John-Nirenberg inequality using a novel Bellman function, advancing the understanding of function space inequalities.

## Contribution

It introduces a new Bellman function to compute sharp constants in the symmetric integral form of the John-Nirenberg inequality, providing precise bounds.

## Key findings

- Sharp constants determined for the inequality
- Introduction of a new Bellman function
- Enhanced understanding of function space bounds

## Abstract

We find sharp constants in the symmetric integral form of the John-Nirenberg inequality. The result is based upon computation of a new interesting Bellman function.