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 Ap-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, ∞), | • |, x 2λ dx).x d dx on (0, ∞). h λ , # λ and λ τ x , x ∈ (0, ∞), are connected with ∆ λ . For every f, g ∈ S(0, ∞), the Schwartz space on (0, ∞), we have that