2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75923We 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.28 pagesProbability47D03, 31C05Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplaciantext