The best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$
Functional Analysis
2018-04-04 v2
Abstract
We compute the best constant in the embedding of into , extending a result of Humbert and Nazaret in dimensions one and two to any . The main tool is the identification of as a fundamental solution of a certain elliptic operator of order .
Keywords
Cite
@article{arxiv.1706.06928,
title = {The best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$},
author = {Itai Shafrir},
journal= {arXiv preprint arXiv:1706.06928},
year = {2018}
}