We introduce potential spaces on fractal metric spaces, investigate their embedding theorems, and derive various Besov spaces. Our starting point is that there exists a local, stochastically complete heat kernel satisfying a two-sided estimate on the fractal considered.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-4,
author = {Jiaxin Hu and Martina Z\"ahle},
title = {Potential spaces on fractals},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {259-281},
zbl = {1119.31008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-4}
}
Jiaxin Hu; Martina Zähle. Potential spaces on fractals. Studia Mathematica, Tome 166 (2005) pp. 259-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-4/