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

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^{2lambda }dx).