The Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem

TL;DR

This paper offers an alternative proof and explicit expression for the Bellman function associated with the dyadic maximal operator, linking it to the Dyadic Carleson Imbedding Theorem, and evaluates its four-variable form.

Contribution

It provides a new proof and explicit formula for the Bellman function of the dyadic maximal operator, enhancing understanding of its connection to the Dyadic Carleson Imbedding Theorem.

Findings

Derived an explicit expression for the Bellman function

Connected the Bellman function to the Dyadic Carleson Imbedding Theorem

Evaluated the Bellman function in four variables

Abstract

We provide an alternative proof and expression of the Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem, which appears in [10]. We also evaluate the Bellman function of four variables of the dyadic maximal operator