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Compactness Results for a Class of Limiting Interpolation Methods

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Abstract

We study the behavior of compact operators when we interpolate them by real methods defined through slowly varying functions and rearrangement invariant spaces. We apply these results to prove compactness of certain integral operators acting between grand Lebesgue spaces and between small Lebesgue spaces.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30071, Espinardo (Murcia), Spain

    Pedro Fernández-Martínez & Teresa Signes

  2. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040, Madrid, Spain

    Alba Segurado

Authors
  1. Pedro Fernández-Martínez
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  2. Alba Segurado
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  3. Teresa Signes
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Corresponding author

Correspondence to Pedro Fernández-Martínez.

Additional information

This work was supported by the Spanish Ministerio de Economía y Competitividad (MTM2013-42220-P) and Fundación Séneca de la Región de Murcia 19378/PI/14.

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Fernández-Martínez, P., Segurado, A. & Signes, T. Compactness Results for a Class of Limiting Interpolation Methods. Mediterr. J. Math. 13, 2959–2979 (2016). https://doi.org/10.1007/s00009-015-0667-3

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  • DOI: https://doi.org/10.1007/s00009-015-0667-3

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