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The Poincare inequality is an open ended condition

Keith, Stephen; Zhong, Xiao


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.

CollectionsANU Research Publications
Date published: 2008
Type: Journal article
Source: Annals of Mathematics


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