Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces

Katarzyna Pietruska-Pałuba. "Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces." Bulletin of the Polish Academy of Sciences. Mathematics 56.3 (2008): 257-299. <http://eudml.org/doc/281230>.

@article{KatarzynaPietruska2008,
abstract = {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.},
author = {Katarzyna Pietruska-Pałuba},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Gagliardo seminorm; stable process; Dirichlet form; fractional diffusion},
language = {eng},
number = {3},
pages = {257-299},
title = {Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces},
url = {http://eudml.org/doc/281230},
volume = {56},
year = {2008},
}

TY - JOUR
AU - Katarzyna Pietruska-Pałuba
TI - Limiting Behaviour of Dirichlet Forms for Stable Processes on Metric Spaces
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 3
SP - 257
EP - 299
AB - 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.
LA - eng
KW - Gagliardo seminorm; stable process; Dirichlet form; fractional diffusion
UR - http://eudml.org/doc/281230
ER -