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

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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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Authors and Affiliations

  1. Instituto de Matemática Aplicada del Litoral CONICET-UNL, Santa Fe, Argentina

    B. Bongioanni, A. Cabral & E. Harboure

Authors
  1. B. Bongioanni
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  2. A. Cabral
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  3. E. Harboure
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Correspondence to B. Bongioanni.

Additional information

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

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