Sharp affine weighted $L^p$ Sobolev type inequalities
Functional Analysis
2017-09-01 v1
Abstract
We establish sharp affine weighted Sobolev type inequalities by using the Busemann-Petty centroid inequality proved by Lutwak, Yang and Zhang. Our approach consists in combining in a convenient way the latter one with a suitable family of sharp weighted Sobolev type inequalities obtained by Nguyen and allows to characterize all extremizers in some cases. The new inequalities don't rely on any euclidean geometric structure.
Cite
@article{arxiv.1708.09471,
title = {Sharp affine weighted $L^p$ Sobolev type inequalities},
author = {Julian Haddad and Carlos Hugo Jiménez and Marcos Montenegro},
journal= {arXiv preprint arXiv:1708.09471},
year = {2017}
}