Authors
Citation
L. Saloffcoste, ON GLOBAL SOBOLEV INEQUALITIES, Forum mathematicum, 6(3), 1994, pp. 271-286
Citations number
31
Categorie Soggetti
Mathematics,Mathematics,Mathematics
Journal title
ISSN journal
09337741
Volume
6
Issue
3
Year of publication
1994
Pages
271 - 286
Database
ISI
SICI code
0933-7741(1994)6:3<271:OGSI>2.0.ZU;2-3
Abstract
In the Euclidean space R(n), n greater-than-or-equal-to 2, if a functi
on f has an integrable gradient, there exists a constant A (f) such th
at f - A (f) is in L(n/(n-1)). We study this question in a rather gene
ral setting. The main result specializes to Lie groups having polynomi
al volume growth, yielding a simple proof of a recent theorem of G. Al
exopoulos and N. Lohoue.