The Poincaré inequality is an open ended condition

Stephen Keith, Xiao Zhong

Type: Article

Publication Date: 2008-03-01

Citations: 200

DOI: https://doi.org/10.4007/annals.2008.167.575

Abstract

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.

Locations

Annals of Mathematics - View - PDF

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