Resumen de Subelliptic Poincaré inequalities: the case p < 1

Pekka Koskela, Guozhen Lu, Stephen M. Buckley

• We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for $p<1$ under some assumptions on the subelliptic gradient of the function. Such inequalities hold on Boman domains associated with the underlying Carnot-Carathéodory metric. In particular, they remain true for solutions to certain classes of subelliptic equations. Our results complement the earlier results in these directions for $p\ge 1$.