English

On the weighted inequality between the Gagliardo and Sobolev seminorms

Classical Analysis and ODEs 2023-02-28 v1 Analysis of PDEs

Abstract

We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With A1A_1 weights we improve earlier results of Bourgain, Brezis, and Mironescu.

Keywords

Cite

@article{arxiv.2302.14029,
  title  = {On the weighted inequality between the Gagliardo and Sobolev seminorms},
  author = {Ritva Hurri-Syrjänen and Javier C. Martínez-Perales and Carlos Pérez and Antti V. Vähäkangas},
  journal= {arXiv preprint arXiv:2302.14029},
  year   = {2023}
}