Mathematical Research Letters

Volume 16 (2009)

Number 3

Subelliptic Bourgain–Brezis estimates on groups

Pages: 487 – 501



Sagun Chanillo (Rutgers)

Jean van Schaftingen (Université catholique de Louvain)


We show that divergence-free $\mathrm{L}^1$ vector fields on a nilpotent homogeneous group of homogeneous dimension $Q$ are in the dual space of functions whose gradient is in $\mathrm{L}^Q$. This was previously obtained on $\R^n$ by Bourgain and Brezis.

Published 1 January 2009