Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces

• Autorzy: Katarzyna Pietruska-Pałuba
• Języki publikacji: EN

Abstrakty

EN

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
$1/C ℰ(f,f) ≤ lim inf_{σ↗1} (1−σ)||f||_{W^{σ,2}} ≤ lim sup_{σ↗1}(1−σ) ||f||_{W^{σ,2}} ≤ Cℰ(f,f)$,
where ℰ is the Dirichlet form relative to the fractional diffusion.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 3
• Strony: 257-299

Daty

wydano

2008

Twórcy

autor

Katarzyna Pietruska-Pałuba

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba56-3-8