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.
Keywords:
paper devoted spaces generalized smoothness so called h sets first quarkonial representations isotropic spaces generalized smoothness mathbb h set investigate representations spaces via differences which helpful want explicit representation domain dirichlet form h sets prove representations equivalent domain time changed dirichlet form h set
Affiliations des auteurs :
V. Knopova
1
;
M. Zähle
1
1
Mathematical Institute University of Jena Ernst-Abbe-Platz 2 07743 Jena, Germany
@article{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},
pages = {277--308},
year = {2006},
volume = {174},
number = {3},
doi = {10.4064/sm174-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm174-3-4/}
}
TY - JOUR
AU - V. Knopova
AU - M. Zähle
TI - Spaces of generalized smoothness on $h$-sets
and related Dirichlet forms
JO - Studia Mathematica
PY - 2006
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EP - 308
VL - 174
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm174-3-4/
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%A M. Zähle
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and related Dirichlet forms
%J Studia Mathematica
%D 2006
%P 277-308
%V 174
%N 3
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%R 10.4064/sm174-3-4
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V. Knopova; M. Zähle. Spaces of generalized smoothness on $h$-sets
and related Dirichlet forms. Studia Mathematica, Tome 174 (2006) no. 3, pp. 277-308. doi: 10.4064/sm174-3-4
