Subelliptic Bourgain-brezis Estimates On Groups

Chanillo, Sagun;Van Schaftingen, Jean
(2009) Mathematical Research Letters — Vol. 16, n° 2-3, p. 487-501 (2009)

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We show that divergence-free L-1 vector fields on a nilpotent homogeneous group of homogeneous dimension Q are in the dual space of functions whose gradient is in L-Q. This was previously obtained on R-n by Bourgain and Brezis.
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Chanillo, S., & Van Schaftingen, J. (2009). Subelliptic Bourgain-brezis Estimates On Groups. Mathematical Research Letters, 16(2-3), 487-501. https://doi.org/10.4310/MRL.2009.v16.n3.a9 (Original work published 2009)