Optimal rearrangement invariant Sobolev embeddings in mixed norm spaces
Functional Analysis
2015-10-06 v2
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<n), and by Hansson, Brezis and Wainger and Maz'ya (p=n) can be further strengthened by considering mixed norms on the target spaces.
Keywords
Cite
@article{arxiv.1406.7760,
title = {Optimal rearrangement invariant Sobolev embeddings in mixed norm spaces},
author = {Nadia Clavero and Javier Soria},
journal= {arXiv preprint arXiv:1406.7760},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1402.6460