In this talk, I will talk about the approximation of non-isotropic $\dot{NL}^{1,Q}$ functions by $L^\infty$ functions on stratified homogeneous groups, generalizing a result of Bourgain-Brezis. I will then present some applications of this result, including how to derive a divergence-curl inequality for $\bar{\partial}_b$ on Heisenberg group $H^n$.
This is a joint work with Po-Lam Yung.