Subelliptic Bourgain-Brezis Estimates on Groups

Abstract

We show that divergence free vector fields which belong to L^1 on stratified, nilpotent groups are in the dual space of functions whose sub-gradient are L^Q integrable where Q is the homogeneous dimension of the group. This was first obtained on Euclidean space by Bourgain and Brezis.

15 pages, v2 has some typos fixed in lemma 2.1

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