Calder\'on-Zygmund operators in the Bessel setting

TL;DR

This paper investigates key harmonic analysis operators associated with Bessel operators, demonstrating they are Calderón-Zygmund operators in a space of homogeneous type, which clarifies their mapping properties.

Contribution

It establishes that various fundamental Bessel-related harmonic analysis operators are Calderón-Zygmund operators, extending the theory to the Bessel setting.

Findings

Operators are Calderón-Zygmund in the Bessel setting

Mapping properties follow from general Calderón-Zygmund theory

Includes maximal operators, square functions, multipliers, and Riesz transforms

Abstract

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.