### Hajłasz-Sobolev type spaces and $p$-energy on the Sierpinski gasket.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

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.

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.

**Page 1**