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

被引：6
|
作者：
Baldi, Annalisa [1 ]
Franchi, Bruno [1 ]
Pansu, Pierre [2 ]
机构：
[1] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy
[2] Univ Paris Saclay, Lab Math Orsay, CNRS, F-91405 Orsay, France
来源：
ADVANCES IN MATHEMATICS | 2020年 / 366卷
基金：
英国工程与自然科学研究理事会;
关键词：
Heisenberg groups; Differential forms; Sobolev-Poincare inequalities; Contact manifolds; Homotopy formula; SOBOLEV INEQUALITIES; CARNOT GROUPS; DOMAINS; EXTENSION; EQUATIONS; REPRESENTATION; OPERATORS; THEOREMS; SYSTEMS;
D O I：
10.1016/j.aim.2020.107084
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove interior Poincare 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. (C) 2020 Elsevier Inc. All rights reserved.
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页数：53
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