L~1-Poincaré and Sobolev inequalities for differential forms in Euclidean spaces Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

In this paper, we prove Poincaré and Sobolev inequalities for differential forms in L~1(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 and Brezis(2007).