We consider post-critically finite self-similar fractals with regular harmonic structures. We first obtain effective resistance estimates in terms of the Euclidean metric, which in particular imply the embedding theorem for the domains of the Dirichlet forms associated with the harmonic structures. We then characterize the domains of the Dirichlet forms.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-5,
author = {Jiaxin Hu and Xingsheng Wang},
title = {Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {153-172},
zbl = {1114.28007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-5}
}
Jiaxin Hu; Xingsheng Wang. Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals. Studia Mathematica, Tome 173 (2006) pp. 153-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-5/