A note on the Moser-Trudinger inequality in Sobolev-Slobodeckij spaces in dimension one

Stefano Iula

A note on the Moser-Trudinger inequality in Sobolev-Slobodeckij spaces in dimension one

Analysis of PDEs 2016-10-05 v1

Authors: Stefano Iula

Abstract

We discuss some recent results by Parini and Ruf on a Moser-Trudinger type inequality in the setting of Sobolev-Slobodeckij spaces in dimension one. We push further their analysis considering the inequality on the whole $\mathbb{R}$ and we give an answer to one of their open questions.

Keywords

Moser-Trudinger inequality Sobolev-Slobodeckij space fractional Sobolev space sharp constant dimension one

Cite

@article{arxiv.1610.00933,
  title  = {A note on the Moser-Trudinger inequality in Sobolev-Slobodeckij spaces in dimension one},
  author = {Stefano Iula},
  journal= {arXiv preprint arXiv:1610.00933},
  year   = {2016}
}

Comments

12 pages

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