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/