Optimal rearrangement invariant Sobolev embeddings in mixed norm spaces

2014/06/30 by Nadia Clavero, Javier Soria, Clavero, Nadia +1
Engineering · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1406.7760

openalex publication_date 2014/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We improve the Sobolev-type embeddings due to Gagliardo and Nirenberg in the setting of rearrangement invariant (r.i.) spaces. In particular we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space by Poornima, O'Neil and Peetre (1 <=p

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