Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces

Katarzyna Pietruska-Pałuba

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008), p. 257-299 / Harvested from The Polish Digital Mathematics Library

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Résumé

Supposing that the metric space in question supports a fractional diffusion, we prove that after introducing an appropriate multiplicative factor, the Gagliardo seminorms ${| | f | |}_{W^{σ, 2}}$ of a function f ∈ L²(E,μ) have the property $1 / C ℰ (f, f) \leq l i m i n f_{σ ↗ 1} {(1 - σ) | | f | |}_{W^{σ, 2}} \leq l i m s u p_{σ ↗ 1} {(1 - σ) | | f | |}_{W^{σ, 2}} \leq C ℰ (f, f)$ , where ℰ is the Dirichlet form relative to the fractional diffusion.

Publié le : 2008-01-01

Zbl 1165.60029

EUDML-ID : urn:eudml:doc:281230

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     year = {2008},
     pages = {257-299},
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Katarzyna Pietruska-Pałuba. Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 257-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-8/