  We consider fully nonlinear integro-differential equations governed by
kernels that have different homogeneities in different directions. We prove a
nonlocal version of the ABP estimate, a Harnack inequality and the interior
$C^{1, \gamma}$ regularity, extending the results of [Caffarelli and Silvestre,
CPAM 62, 2009] to the anisotropic case.
