Subelliptic Poincaré inequalities: the case \(p<1\)
type: Item
instance of: scholarly article
title: Subelliptic Poincaré inequalities: the case \(p<1\)
zbMATH Open document ID: 0895.26005
DOI: 10.5565/PUBLMAT_39295_08
author: Pekka Koskela
author: Guozhen Lu
author: S. M. Buckley
published in: Publicacions Matemàtiques
publication date: 1996-08-04T00:00:00Z
full work available at URL: https://eudml.org/doc/41233
review text: The paper is devoted to the Poincaré-type inequality \[ \biggl(\frac 1{| B| }\int_B| f(x)-f_B| ^q\,dx\biggr)^{1/q}\leq Cr\Biggl( \frac 1{| B| }\int_B\biggl(\sum_j| \langle X_j,\nabla f(x)\rangle| ^2\biggr)^{p/2}\Biggr)^{1/p}, \] where \(0<p<1\), \(q>p\) is tied to \(p\) by a natural balance condition, \(\{X_j\}\) is a finite collection of smooth vector fields satisfying the Hörmander condition, and the subelliptic gradient of \(f\) satisfies certain weak reverse Hölder condition. The point here is that \(p<1\); in this case general Poincaré-type results are almost impossible to get, but it turns out that under the weak reverse Hölder condition imposed on \(\nabla f\) the above inequality holds. Weighted cases are treated, too.
reviewed by: Luboš Pick
Mathematics Subject Classification ID: 35H20
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 889852
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: weak reverse Hölder condition
zbMATH Keywords: the case \(p<1\)
zbMATH Keywords: subelliptic gradient
zbMATH Keywords: Hörmander condition
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 889852