  We are dealing with possibly degenerate second-order parabolic operators
whose coefficients are infinitely differentiable with respect to space
variables and only measurable with respect to the time variable. We impose the
H\"ormander condition on the diffusion coefficients and prove that the
solutions of the corresponding equations with right-hand sides which are
infinitely differentiable in the space variables in a space-time domain have
also this property.

Analysis of PDEs