The Poincaré inequality is an open ended condition

2008/03/01 by Stephen Keith, Xiao Zhong · 15 citations
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.4007/annals.2008.167.575

Abstract

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

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