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

Issue

Vol. 95 No. 2 (2004)

Section

Articles

How to Cite

[1]
S. Keith and K. Rajala, “A remark on Poincaré inequalities on metric measure spaces”, Math. Scand., vol. 95, no. 2, pp. 299–304, Dec. 2004, doi: 10.7146/math.scand.a-14461.