Weighted norm inequalities for the maximal functions associated to a critical radius function on variable Lebesgue spaces

Abstract

In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the Schrödinger operator L=−Δ+V in Rd, where V a non-negative potential which satisfying a some specific reverse Hölder condition. We consider new classes of weights that locally behave as the Muckenhoupt class for Lebesgue spaces with variable exponents considered in [6] and actually including them.