A Cotlar Type Maximal Function Associated With Fourier Multipliers

TL;DR

This paper establishes the boundedness of a maximal operator linked to Fourier multipliers using dyadic frequency decomposition, under minimal regularity conditions, advancing understanding of Fourier analysis techniques.

Contribution

It introduces a Cotlar type maximal function framework for Fourier multipliers with weak regularity assumptions, expanding the scope of boundedness results.

Findings

Proves $L^p$ boundedness of the maximal operator

Works under weak regularity assumptions

Extends classical Fourier multiplier theory

Abstract

We prove the $L^p$ boundedness of a maximal operator associated with a dyadic frequency decomposition of a Fourier multiplier, under a weak regularity assumption.