The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-1,
author = {Alireza Ranjbar-Motlagh},
title = {A note on the Poincar\'e inequality},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {1-11},
zbl = {1037.26012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-1}
}
Alireza Ranjbar-Motlagh. A note on the Poincaré inequality. Studia Mathematica, Tome 157 (2003) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-1/