Positivity

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

Integrable cross sections in mixed-norm spaces and Sobolev embeddings

Article

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.

Keywords

Rearrangement-invariant spaces Mixed-norm spaces Embeddings Lorentz spaces 

Mathematics Subject Classification

46E35 46E30 

Notes

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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Copyright information

© Springer Basel 2015

Authors and Affiliations

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

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