$L^1$-Poincaré and Sobolev inequalities for differential forms in Euclidean spaces

Abstract

In this paper, we prove Poincaré and Sobolev inequalities for differential forms in $L^1({\mathbb{R}}^n)$. The singular integral estimates that it is possible to use for $L^p$, $p>1$, are replaced here with inequalities which go back to Bourgain-Brezis.

Accepted for publication in Science China Mathematics. arXiv admin note: text overlap with arXiv:1902.04819