We use the Calderón Maximal Function to prove the Kato-Ponce Product Rule Estimate and the Christ-Weinstein Chain Rule Estimate for the Hajłasz gradient on doubling measure metric spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-2,
author = {A. Eduardo Gatto and Carlos Segovia},
title = {Product rule and chain rule estimates for the Haj\l asz gradient on doubling metric measure spaces},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {19-24},
zbl = {1106.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-2}
}
A. Eduardo Gatto; Carlos Segovia. Product rule and chain rule estimates for the Hajłasz gradient on doubling metric measure spaces. Colloquium Mathematicae, Tome 106 (2006) pp. 19-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-2/