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.
Baldi A., Franchi B., Pansu P. (2020). L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups. ADVANCES IN MATHEMATICS, 366, 1-53 [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.| File | Dimensione | Formato | |
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BFP3_final_revised.pdf
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BFP_preprint.pdf
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