We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space by functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for on the Heisenberg group .
Cite this article
Yi Wang, Po-Lam Yung, A subelliptic Bourgain–Brezis inequality. J. Eur. Math. Soc. 16 (2014), no. 4, pp. 649–693