  This note presents a proof that the non-tangential maximal function of the
Ornstein-Uhlenbeck semigroup is bounded almost surely by the Gaussian
Hardy-Littlewood maximal function. In particular this entails improvement on a
result by Pineda and Urbina who proved a similar result for a `trunctated'
version of the non-tangential maximal function. We actually obtain boundedness
of the maximal function on non-tangential cones of arbitrary aperture.
