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 L1 norm. Unlike for Lp, 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.

L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups / Baldi A.; Franchi B.; Pansu P.. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 366:(2020), pp. 107084.1-107084.53. [10.1016/j.aim.2020.107084]

L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups

Baldi A.;Franchi B.
;
2020

Abstract

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 L1 norm. Unlike for Lp, 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.
2020
L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups / Baldi A.; Franchi B.; Pansu P.. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 366:(2020), pp. 107084.1-107084.53. [10.1016/j.aim.2020.107084]
Baldi A.; Franchi B.; Pansu P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/756943
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