Mapping properties of fundamental operators in harmonic analysis related to Bessel operators

TL;DR

This paper establishes sharp weighted inequalities for various fundamental harmonic analysis operators associated with Bessel operators, including maximal functions, Riesz transforms, and square functions.

Contribution

It provides the first sharp power-weighted bounds for these operators in the context of Bessel-related harmonic analysis.

Findings

Sharp strong and weak type inequalities proved

Weighted bounds are optimal and precise

Results extend understanding of harmonic analysis with Bessel operators

Abstract

We prove sharp power-weighted strong type, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.