A subelliptic Bourgain–Brezis inequality

  • Yi Wang

    Stanford University, USA
  • Po-Lam Yung

    Rutgers University, Piscataway, USA


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

Cite this article

Yi Wang, Po-Lam Yung, A subelliptic Bourgain–Brezis inequality. J. Eur. Math. Soc. 16 (2014), no. 4, pp. 649–693

DOI 10.4171/JEMS/443