Affine Hardy--Littlewood--Sobolev inequalities
Metric Geometry
2025-09-29 v3 Functional Analysis
Abstract
Sharp affine Hardy--Littlewood--Sobolev inequalities for functions on are established, which are significantly stronger than (and directly imply) the sharp Hardy--Littlewood--Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu. In addition, sharp reverse inequalities for the new inequalities and the affine fractional Sobolev inequalities are obtained for log-concave functions on .
Keywords
Cite
@article{arxiv.2212.12194,
title = {Affine Hardy--Littlewood--Sobolev inequalities},
author = {Julián Haddad and Monika Ludwig},
journal= {arXiv preprint arXiv:2212.12194},
year = {2025}
}