  Let M be a globally Riemannian symmetric space. We prove a duality estimate
between pairings of vector fields with divergence zero and and in L^1 with
vector fields in a critical Sobolev space on M. As a consequence we get a sharp
Calderon-Zygmund estimate for solutions to Poisson's equation on M, where the
right side data is manufactured from divergence free vector fields which are in
L^1. Such a result was proved earlier by Jean Bourgain and Haim Brezis on
Euclidean space.
