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In this paper, we prove interior Poincaré 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.1991 Mathematics Subject Classification. 58A10, 35R03, 26D15, 43A80, 46E35, 35F35.

This paper is divided in two parts: in Section 2 we define recursively a privileged basis of the primitive forms in a symplectic space (V 2n , ω). Successively, in Section 3 we apply our construction in the setting of Heisenberg groups H n , n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin's complex of differential forms in H n .