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math.PR2008
Estimates of tempered stable densities
Paweł Sztonyk
Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding Lévy measure and the Lévy--Khinchin exponent. The…
math.PR2007★ 4 cited
Regularity of harmonic functions for anisotropic fractional Laplacian
Paweł Sztonyk
We prove that bounded harmonic functions of anisotropic fractional Laplacians are Hölder continuous under mild regularity assumptions on the corresponding Lévy measure. Under some…
math.PR2005★ 7 cited
Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian
Krzysztof Bogdan, Paweł Sztonyk
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also…