Some of the arguments and techniques developed by the authors in a previous paper are applied to the study of the boundedness of certain operators associated with the Ornstein–Uhlenbeck semigroup. In particular, a simple proof is given of the weak type 1 with respect to the Gaussian measure of the Riesz transforms of order 1 and the Littlewood–Paley g-function which then is extended to show the same property for the Riesz transforms of order 2. For Riesz transforms of higher order boundedness is shown in appropriate spaces close to L1.