Subelliptic Poincaré inequalities: the case p < 1

Buckley, S. and Koskela , P. and Lu, G. (1995) Subelliptic Poincaré inequalities: the case p < 1. Publicacions Matemàtiques, 39 (2). pp. 313-334. ISSN 0214-1493

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We obtain (weighted) Poincaré type inequalities for vector elds 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.

Item Type: Article
Keywords: Subelliptic Poincaré inequalities; vector fields; Hörmander condition; Boman domains; Carnot-Carathéodory metric; subelliptic equations.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1630
Depositing User: Prof. Stephen Buckley
Date Deposited: 03 Nov 2009 10:42
Journal or Publication Title: Publicacions Matemàtiques
Publisher: Universitat Autònoma Barcelona
Refereed: No
Funders: NSF Grant DMS-9207715, NSF Grant DMS-9305742, Academy of Finland, NSF Grant DMS-9315963

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