Sharp integral inequalities for the dyadic maximal operator and applications

TL;DR

This paper establishes a precise integral inequality for the dyadic maximal operator, linking the integrals of a function and its maximal function, with potential applications in harmonic analysis.

Contribution

It introduces a sharp integral inequality for the dyadic maximal operator, enhancing understanding of its behavior and applications.

Findings

Proved a sharp integral inequality for the dyadic maximal operator

Connected integrals of functions and their dyadic maximal functions

Potential applications in harmonic analysis and related fields

Abstract

We prove a sharp integral inequality for the dyadic maximal operator, connecting integrals of $\phi$, and of the dyadic maximal function of $\phi$.