  It is well known that the transition semigroup of an Ornstein Uhlenbeck
process with delay is not strong Feller for small times, so it has no
regularizing effects when acting on bounded and continuous functions. In this
paper we study regularizing properties of this transition semigroup when acting
on special functions of the past trajectory. With this regularizing property,
we are able to prove existence and uniqueness of a mild solution for a special
class of semilinear Kolmogorov equations; we apply these results to a
stochastic optimal control problem.
