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 ℝⁿ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-4,
author = {V. Knopova and M. Z\"ahle},
title = {Spaces of generalized smoothness on h-sets and related Dirichlet forms},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {277-308},
zbl = {1104.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-4}
}
V. Knopova; M. Zähle. Spaces of generalized smoothness on h-sets and related Dirichlet forms. Studia Mathematica, Tome 173 (2006) pp. 277-308. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-4/