, Volume 20, Issue 2, pp 435–466 | Cite as

Integrable cross sections in mixed-norm spaces and Sobolev embeddings

  • Nadia ClaveroEmail author
  • Javier Soria


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.


Rearrangement-invariant spaces Mixed-norm spaces Embeddings Lorentz spaces 

Mathematics Subject Classification

46E35 46E30 



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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© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Applied Mathematics and AnalysisUniversity of BarcelonaBarcelonaSpain

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