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Limiting behaviour of Dirichlet forms for stable processes on metric spaces

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Warianty tytułu
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 ||ƒ||wσ,2 of a function ƒ ∈ L²(E, μ) have the property [wzór...] where ε is the Dirichlet form relative to the fractional diffusion.
Słowa kluczowe
Rocznik
Strony
257--266
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Institute of Mathematics, University of Warsaw, Banacha 2 02-097 Warszawa, Poland, kpp@mimuw.edu.pl
Bibliografia
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  • [7] —, —, —, Limiting embedding theorems for Ws,p when s ↑ 1 and applications, J. Anal. Math. 87 (2002), 77-101.
  • [8] H. Brézis, How to recognize constant functions, Uspekhi Mat. Nauk, 57 (2002), no. 4, 59-74 (in Russian); English transl.: Russian Math. Surveys 57 (2002), 693-708.
  • [9] E. A. Carlen, S. Kusuoka and D. W. Stroock, Upper bounds for symmetric Markov transition functions, Ann. Inst. Poincare Probab. Statist. 23 (1987), 245-287.
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  • [14] A. Grigoryan and T. Kumagai, On the dichotomy of the heat kernel two sided-estimates, in: Proc. Sympos. Pure Math. 77, Amer. Math. Soc., 2008, 199-210.
  • [15] B. M. Hambly and T. Kumagai, Transition density estimates for diffusion processes on post critically finite self-similar fractals, Proc. London. Math. Soc. 78 (1999), 431-458.
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  • [17] T. Kumagai, Function spaces and stochastic processes on fractals, in: Fractal Geometry and Stochastics III, C. Bandt et al. (eds.), Progr. Probab. 57, Birkhäuser, 2004, 221-234.
  • [18] W. Masja [V. Maz’ya] und J. Nagel, Über äquivalente Normierung der anisotropen Funktionalräume Hμ(Rn), Beiträge Anal. 12 (1978), 7-17.
  • [19] K. Pietruska-Pałuba, On function spaces related to fractional diffusions on d-sets, Stoch. Stoch. Rep. 70 (2000), 153-164.
  • [20] —, Heat kernels on metric spaces and a characterization of constant functions, Manuscripta Math. 115 (2004), 389-399.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0035-0008
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