Extremal sequences for the Bellman function of the dyadic maximal operator

TL;DR

This paper characterizes extremal sequences for the Bellman function of the dyadic maximal operator, showing they behave like eigenfunctions corresponding to a specific eigenvalue, advancing understanding of the operator's extremal behavior.

Contribution

It provides a new characterization of extremal sequences for the Bellman function, linking them to eigenfunction-like behavior for the dyadic maximal operator.

Findings

Extremal sequences behave approximately like eigenfunctions.

Characterization of extremal sequences for the Bellman function.

Insight into the spectral properties of the dyadic maximal operator.

Abstract

We give a characterization of the extremal sequences for the Bellman function of the dyadic maximal operator.In fact we prove that they behave approximately like eigenfunctions of this operator for a specific eigenvalue.