Mathematical Research Letters

Volume 16 (2009)

Number 3

Subelliptic Bourgain–Brezis estimates on groups

Pages: 487 – 501

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n3.a9

Authors

Sagun Chanillo (Rutgers)

Jean van Schaftingen (Université catholique de Louvain)

Abstract

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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