$L^1$-Poincar\'e inequalities for differential forms on Euclidean spaces and Heisenberg groups
Differential Geometry
2019-02-14 v1
Abstract
In this paper, we prove interior Poincar{\'e} and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differential of a differential form is measured in L 1 norm. Unlike for L p , p > 1, the estimates are doomed to fail in top degree. The singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis in Euclidean spaces, and to Chanillo-van Schaftingen in Heisenberg groups.
Keywords
Cite
@article{arxiv.1902.04819,
title = {$L^1$-Poincar\'e inequalities for differential forms on Euclidean spaces and Heisenberg groups},
author = {Annalisa Baldi and Bruno Franchi and Pierre Pansu},
journal= {arXiv preprint arXiv:1902.04819},
year = {2019}
}