  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
$\mathbb{H}^n$.
