English

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 WN,1(RN)W^{N,1}({\mathbb R}^N) into L(RN)L^\infty({\mathbb R}^N), extending a result of Humbert and Nazaret in dimensions one and two to any NN. The main tool is the identification of logx\log |x| as a fundamental solution of a certain elliptic operator of order 2N2N.

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}
}