Subelliptic Bourgain–Brezis estimates on groups

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.

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Published 1 January 2009