TY - JOUR

T1 - The Poincaré inequality is an open ended condition

AU - Keith, Stephen

AU - Xiao, Zhong

PY - 2008/3

Y1 - 2008/3

N2 - Let p > 1 and let (X, d, μ) be a complete metric measure space with μ Borel and doubling that admits a (1, p)-Poincaré inequality. Then there exists ε > 0 such that (X, d, μ) admits a (1, q)-Poincaré inequality for every q > p -ε, quantitatively.

AB - Let p > 1 and let (X, d, μ) be a complete metric measure space with μ Borel and doubling that admits a (1, p)-Poincaré inequality. Then there exists ε > 0 such that (X, d, μ) admits a (1, q)-Poincaré inequality for every q > p -ε, quantitatively.

UR - http://www.scopus.com/inward/record.url?scp=49749131648&partnerID=8YFLogxK

U2 - 10.4007/annals.2008.167.575

DO - 10.4007/annals.2008.167.575

M3 - Article

SN - 0003-486X

VL - 167

SP - 575

EP - 599

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -