Resumen de The Poincaré inequality is an open ended condition

Stephen Keith, Xiao Zhong

• 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 e > 0 such that (X,d,µ) admits a (1,q)-Poincaré inequality for every q > p - e, quantitatively.