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Absolutely Continuous Embeddings of Rearrangement-Invariant Spaces

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Abstract

Compactness of embeddings between rearrangement invariant spaces is closely related to absolute continuity of these embeddings. We study absolutely continuous embeddings between rearrangement invariant spaces. In particular it is shown that an absolutely continuous embedding is never optimal. We give sufficient (and under additional hypotheses necessary) conditions for absolute continuity of these embeddings. We also provide quantitative estimates of absolutely continuous embeddings.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, Campus de Espinardo, 30071, Espinardo (Murcia), Spain

    Pedro Fernández-Martínez

  2. Departamento de Matemáticas y Computación, Escuela Politécnica Superior, Universidad de Burgos, 09001, Burgos, Spain

    Antonio Manzano

  3. Department of Mathematics, Technion - Israel institute of Technology, Haifa, 32000, Israel

    Evgeniy Pustylnik

Authors
  1. Pedro Fernández-Martínez
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  2. Antonio Manzano
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  3. Evgeniy Pustylnik
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Corresponding author

Correspondence to Pedro Fernández-Martínez.

Additional information

The first author has been partially supported by Fundación Séneca 08791/PI/08. The first two authors have been partially supported by Ministerio de Educación y Ciencia (MTM2007-62121).

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Fernández-Martínez, P., Manzano, A. & Pustylnik, E. Absolutely Continuous Embeddings of Rearrangement-Invariant Spaces. Mediterr. J. Math. 7, 539–552 (2010). https://doi.org/10.1007/s00009-010-0039-y

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  • DOI: https://doi.org/10.1007/s00009-010-0039-y

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