On a constant related to the Bellman function of three integral variables of the dyadic maximal operator: Part A

TL;DR

This paper investigates the properties of a specific constant related to the Bellman function of three integral variables in the dyadic maximal operator, focusing on its monotonicity with respect to one of the variables.

Contribution

It provides new insights into the monotonicity properties of the constant associated with the Bellman function for the dyadic maximal operator.

Findings

The constant exhibits specific monotonicity behavior with respect to the second variable.

The study advances understanding of the Bellman function's structure in relation to dyadic maximal operators.

Abstract

We study the behaviour of the constant that is provided in the articles [12] and [13], which is connected with the determination of the Bellman function of three integral variables of the dyadic maximal operator. More precisely we study the monotonicity properties of this constant with respect to the second variable from which it depends.