  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.
