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

• Autorzy: Krzysztof Bogdan , Paweł Sztonyk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 60G51: Processes with independent increments; L\'evy processes
• 47D03: Groups and semigroups of linear operators
• 31C05: Harmonic, subharmonic, superharmonic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 2
• Strony: 101-123

Daty

wydano

2007

Twórcy

autor

Krzysztof Bogdan

• Institute of Mathematics, Polish Academy of Sciences
• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Paweł Sztonyk

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm181-2-1