欧几里得空间和海森堡群上differential forms的$L^1$ -Poincaré不等式
$L^1$-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups
摘要：
本文证明了欧几里得空间和海森堡群中的Poincar{é}和Sobolev不等式，在极限情形下，外（分别）Rumin）微分的L1范数度量.与Lp，p > 1的情形不同，该估计在最大程度上注定失败.奇异积分估计被替换为不等式，这些不等式可以追溯到欧几里得空间中的Bourgain-Brezis和海森堡群中的Chanillo-van Schaftingen。
英文摘要：
In this paper, we prove interior Poincar{é} 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.
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