# Sharp and general estimates for the Bellman function of three integral variables related to the dyadic maximal operator

## TL;DR

This paper calculates the Bellman function for three integral variables related to the dyadic maximal operator, providing precise estimates and an upper bound for its domain, advancing understanding of its behavior.

## Contribution

It introduces exact calculations of the Bellman function for three variables and offers an upper bound for its entire domain, extending previous results.

## Key findings

- Computed the Bellman function for three integral variables.
- Provided an upper bound for the Bellman function over its entire domain.
- Enhanced understanding of the dyadic maximal operator's behavior.

## Abstract

We compute the Bellman function of three integral variables associated to the dyadic maximal operator on a subset of its domain. Additionally, we provide an upper bound for the whole domain of its definition.