  We study here the effects of a time-dependent second order perturbation to a
degenerate Ornstein-Uhlenbeck type operator whose diffusive part can be either
local or non-local. More precisely, we establish that some estimates, such as
the Schauder and Sobolev ones, already known for the non-perturbed operator
still hold, and with the same constants, when we perturb the Ornstein-Uhlenbeck
operator with second order diffusions with coefficients only depending on time
in a measurable way. The aim of the current work is twofold: we weaken the
assumptions required on the perturbation in the local case which has been
considered already in [KP17] and we extend the approach presented therein to a
wider class of degenerate Kolmogorov operators with non-local diffusive part of
symmetric stable type.
