Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

TL;DR

This paper establishes sharp weighted inequalities and mapping properties for key harmonic analysis operators linked to the exotic Bessel operator, expanding understanding in this specialized mathematical framework.

Contribution

It provides new sharp inequalities and characterizations for harmonic analysis operators in the exotic Bessel setting, a novel extension of classical results.

Findings

Sharp weighted inequalities for heat semigroup maximal operator

Characterization of mapping properties for Riesz transforms and fractional integrals

Extension of harmonic analysis operator theory to the exotic Bessel framework

Abstract

We prove sharp power-weighted $L^p$, weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator $B_{\nu}$ in the exotic range of the parameter $-\infty < \nu < 1$. Moreover, in the same framework, we characterize basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical $g$-function and fractional integrals (Riesz potential operators).