Two-weighted inequalities for maximal operators related to Schrödinger differential operators

Abstract

We introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman-Stein-type inequalities that connect maximal operators naturally associated to Schrödinger operators.