Extrapolation for Classes of Weights Related to a Family of Operators and Applications

In this work we give extrapolation results on weighted Lebesgue spaces for weights associated to a family of operators. The starting point for the extrapolation can be the knowledge of boundedness on a particular Lebesgue space as well as the boundedness on the extremal case L ^∞. This analysis can be applied to a variety of operators appearing in the context of a Schrödinger operator (??Δ?+?V) where V satisfies a reverse Hölder inequality. In that case the weights involved are a localized version of Muckenhoupt weights.