A subelliptic Bourgain-Brezis inequality

Abstract

We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space ${\dot{NL}}^{1,Q}$ by $L^{\infty }$ functions, generalizing a result of Bourgain-Brezis \cite{MR2293957}. We then use this to obtain a Gagliardo-Nirenberg inequality for ${\bar{\partial }}_b$ on the Heisenberg group ${\mathbb{H}}^n$.

44 pages

References in corpus (3)

• Limiting fractional and Lorentz spaces estimates of differential forms
• Subelliptic Bourgain-Brezis Estimates on Groups
• Estimates for differential operators of vector analysis involving $L^1$-norm