A remark on Poincaré inequalities on metric measure spaces

Stephen Keith; Kai Rajala

doi:10.7146/math.scand.a-14461

A remark on Poincaré inequalities on metric measure spaces

Authors

Stephen Keith
Kai Rajala

DOI:

https://doi.org/10.7146/math.scand.a-14461

Abstract

We show that, in a complete metric measure space equipped with a doubling Borel regular measure, the Poincaré inequality with upper gradients introduced by Heinonen and Koskela [3] is equivalent to the Poincaré inequality with "approximate Lipschitz constants" used by Semmes in [9].

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Published

2004-12-01

How to Cite

Keith, S., & Rajala, K. (2004). A remark on Poincaré inequalities on metric measure spaces. MATHEMATICA SCANDINAVICA, 95(2), 299–304. https://doi.org/10.7146/math.scand.a-14461