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


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. 1 Main results and background Let α ∈ (0, 2) and d ∈ {1, 2, . . .}. We consider an arbitrary Lévy measure on R \ {0… (More)