Quantitative weighted estimates for harmonic analysis operators in the Bessel setting by using sparse domination

TL;DR

This paper establishes quantitative weighted inequalities for harmonic analysis operators in the Bessel setting, using sparse domination techniques to relate operator norms to weight characteristics.

Contribution

It introduces a method to obtain weighted $L^p$ bounds for Bessel convolution operators via sparse domination, extending harmonic analysis tools in this setting.

Findings

Operator norms depend on the $A_p$-characteristic of weights.

Operators are dominated by sparse operators in the Bessel setting.

Quantitative weighted inequalities are established for various harmonic analysis operators.

Abstract

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in terms of the $A_p$-characteristic of the weight $w$. In order to do this we show that the operators under consideration are dominated by a suitable family of sparse operators in the space of homogeneous type $((0,\infty),|\cdot |,x^{2\lambda }dx)$.