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

Stephen Keith^*
, Kai Rajala

^*Corresponding author for this work

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

10 Citations (Scopus)

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 is equivalent to the Poincaré inequality with "approximate Lipschitz constants" used by Semmes in [9].

Original language	English
Pages (from-to)	299-304
Number of pages	6
Journal	Mathematica Scandinavica
Volume	95
Issue number	2
DOIs	https://doi.org/10.7146/math.scand.a-14461
Publication status	Published - 2004

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abstract = "We show that, in a complete metric measure space equipped with a doubling Borel regular measure, the Poincar{\'e} inequality with upper gradients introduced by Heinonen and Koskela is equivalent to the Poincar{\'e} inequality with {"}approximate Lipschitz constants{"} used by Semmes in [9].",

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JO - Mathematica Scandinavica

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A remark on Poincaré inequalities on metric measure spaces

Abstract

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