This note presents a proof that the non-tangential maximal function of the Ornstein-Uhlenbeck semigroup is bounded pointwise by the Gaussian Hardy-Littlewood maximal function. In particular this entails an extension on a result by Pineda and Urbina  who proved a similar result for a 'truncated' version with fixed parameters of the non-tangential maximal function. We actually obtain boundedness of the maximal function on non-tangential cones of arbitrary aperture. \textcopyright 2014 Royal Dutch Mathematical Society (KWG).
A note on Gaussian maximal function
Indagationes Mathematicae 2015;26(1):106-112.