Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian

Tom 181 / 2007

Krzysztof Bogdan, Pawe/l Sztonyk Studia Mathematica 181(2007), 101-123 MSC: Primary 47D03, 31C05; Secondary 60J35, 60G51. DOI: 10.4064/sm181-2-1 Opublikowany online: 1 January 1970

Streszczenie

We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.

Autorzy

  • Krzysztof BogdanInstitute of Mathematics
    Polish Academy of Sciences
    and
    Institute of Mathematics
    Wroc/law University of Technology
    Wybrze/ze Wyspia/nskiego 27
    50-370 Wroc/law, Poland
    e-mail
  • Pawe/l SztonykInstitute of Mathematics
    Wroc/law University of Technology
    Wybrze/ze Wyspia/nskiego 27
    50-370 Wroc/law, Poland
    e-mail

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