Abstract
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.
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This research is partially supported by grants from Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Universidad Nacional del Litoral (UNL), Argentina.
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Bongioanni, B., Cabral, A. & Harboure, E. Extrapolation for Classes of Weights Related to a Family of Operators and Applications. Potential Anal 38, 1207–1232 (2013). https://doi.org/10.1007/s11118-012-9313-x
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DOI: https://doi.org/10.1007/s11118-012-9313-x