Subelliptic Poincaré inequalities: The case $p < 1$

Stephen M. Buckley, Pekka Koskela, G. Lu

Type: Article

Publication Date: 1995-07-01

Citations: 21

DOI: https://doi.org/10.5565/publmat_39295_08

Abstract

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 ≥ 1.

Locations

Publicacions Matemàtiques - View
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Subelliptic Poincaré inequalities: The case $p &lt; 1$