Mathematical Research Letters
Volume 18 (2011)
Local Gagliardo–Nirenberg Estimates for Elliptic Systems of Vector Fields
Pages: 791 – 804
We extend the global $L^1$ estimates proved by Bourgain and Brezis and Lanzani and Stein for the de Rham complex on $\erre^N$ to the setup of local $L^1$ estimates for the differential complex associated to an involutive elliptic structure spanned by a family of linearly independent smooth complex vector fields.