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Journal of the European Mathematical Society

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Volume 16, Issue 4, 2014, pp. 649–693
DOI: 10.4171/JEMS/443

Published online: 2014-04-02

A subelliptic Bourgain–Brezis inequality

Yi Wang[1] and Po-Lam Yung[2]

(1) Stanford University, USA
(2) 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 $\dot{NL}^{1,Q}$ by $L^{\infty}$ functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for $\dbarb$ on the Heisenberg group $\mathbb{H}^n$.

Keywords: Div-curl, compensation phenomena, critical Sobolev embedding, homogeneous groups

Wang Yi, Yung Po-Lam: A subelliptic Bourgain–Brezis inequality. J. Eur. Math. Soc. 16 (2014), 649-693. doi: 10.4171/JEMS/443