Square functions and maximal operators associated with radial Fourier multipliers

TL;DR

This paper explores advanced square functions and maximal operators linked to radial Fourier multipliers, providing new endpoint estimates and extending understanding of these harmonic analysis tools.

Contribution

It introduces novel endpoint estimates for square functions and maximal Bochner-Riesz operators related to radial Fourier multipliers, expanding theoretical knowledge.

Findings

New endpoint estimates for square functions

Improved bounds for maximal Bochner-Riesz operators

Extended results to broader classes of radial multipliers

Abstract

We begin with an overview on square functions for spherical and Bochner-Riesz means which were introduced by Eli Stein, and discuss their implications for radial multipliers and associated maximal functions. We then prove new endpoint estimates for these square functions, for the maximal Bochner-Riesz operator, and for more general classes of radial Fourier multipliers.