The best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$

Itai Shafrir

doi:10.1007/s11118-018-9695-5

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arXiv · 1706.06928

The best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$

Itai Shafrir

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Abstract

We compute the best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$, extending a result of Humbert and Nazaret in dimensions one and two to any $N$. The main tool is the identification of $\log |x|$ as a fundamental solution of a certain elliptic operator of order $2N$.

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BibTeX RIS

Itai Shafrir. 2018-02-14. The best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$. https://doi.org/10.1007/s11118-018-9695-5

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