Spaces of generalized smoothness on -sets and related Dirichlet forms
Tom 174 / 2006
Studia Mathematica 174 (2006), 277-308
MSC: 46E35, 42B35, 28A80, 60J75.
DOI: 10.4064/sm174-3-4
Streszczenie
The paper is devoted to spaces of generalized smoothness on so-called h-sets. First we find quarkonial representations of isotropic spaces of generalized smoothness on \mathbb{R}^n and on an h-set. Then we investigate representations of such spaces via differences, which are very helpful when we want to find an explicit representation of the domain of a Dirichlet form on h-sets. We prove that both representations are equivalent, and also find the domain of some time-changed Dirichlet form on an h-set.
