The Poincaré inequality is an open ended condition

Stephen Keith; Zhong Xiao

doi:10.4007/annals.2008.167.575

The Poincaré inequality is an open ended condition

Stephen Keith^*
, Zhong Xiao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

184 Citations (Scopus)

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.

Original language	English
Pages (from-to)	575-599
Number of pages	25
Journal	Annals of Mathematics
Volume	167
Issue number	2
DOIs	https://doi.org/10.4007/annals.2008.167.575
Publication status	Published - Mar 2008

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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)-Poincar{\'e} inequality. Then there exists ε > 0 such that (X, d, μ) admits a (1, q)-Poincar{\'e} inequality for every q > p -ε, quantitatively.",

author = "Stephen Keith and Zhong Xiao",

year = "2008",

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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.

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The Poincaré inequality is an open ended condition

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