  We prove a new generation result in $L^1$ for a large class of non-local
operators with non-degenerate local terms. This class contains the operators
appearing in Fokker-Planck or Kolmogorov forward equations associated with
L\'evy driven SDEs, i.e. the adjoint operators of the infinitesimal generators
of these SDEs. As a byproduct, we also obtain a new elliptic regularity result
of independent interest. The main novelty in this paper is that we can consider
very general L\'evy operators, including state-space depending coefficients
with linear growth and general L\'evy measures which can be singular and have
fat tails.
