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/