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Integrable cross sections in mixed-norm spaces and Sobolev embeddings

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Abstract

We characterize optimal Sobolev embeddings in terms of integrable cross sections and mixed-norm spaces, involving general rearrangement-invariant estimates. We also find the optimal domains and ranges for these embeddings.

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Acknowledgments

We would like to thank the referee for his/her careful revision which has improved the final version of this work.

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Authors and Affiliations

  1. Department of Applied Mathematics and Analysis, University of Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Nadia Clavero & Javier Soria

Authors
  1. Nadia Clavero
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  2. Javier Soria
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Corresponding author

Correspondence to Nadia Clavero.

Additional information

N. Clavero and J. Soria have been partially supported by the Grants MTM2013-40985-P (Spanish Government) and 2014SGR289 (Catalan Autonomous Government).

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Clavero, N., Soria, J. Integrable cross sections in mixed-norm spaces and Sobolev embeddings. Positivity 20, 435–466 (2016). https://doi.org/10.1007/s11117-015-0365-1

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  • DOI: https://doi.org/10.1007/s11117-015-0365-1

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