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

Abstract

AbstractIn this paper we obtain quantitative weighted $$L^p$$ L p -inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $$L^p(w)$$ L p ( w ) -operator norms in terms of the $$A_p$$ 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 $$((0,\infty ),|\cdot |,x^{2\lambda }dx)$$ ( ( 0 , ∞ ) , | · | , x 2 λ d x ) .