Calder\'on-Zygmund operators in the Bessel setting for all possible type indices

TL;DR

This paper extends the Calderón-Zygmund theory in the Bessel setting to all type parameters, unifying the boundedness results for various harmonic analysis operators across the entire parameter range.

Contribution

It adapts a technique to show that multiple harmonic analysis operators are Calderón-Zygmund operators for all type parameters in the Bessel setting, broadening previous restricted results.

Findings

Harmonic analysis operators are Calderón-Zygmund for all type parameters

Extension of boundedness results to the full range of bb

Unified framework for operators in the Bessel setting

Abstract

In this paper we adapt the technique developed in [17] to show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, Calder\'on-Zygmund operators for all possible values of type parameter $\lambda$ in this context. This extends the results obtained recently in [7], which are valid only for a restricted range of $\lambda$.