Operators associated with the Ornstein-Uhlenbeck semigroup

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 ass ociated with the Ornstein-Uhlenbeck semigroup. In particular, a simple proo f is given of the weak type 1 with respect to the Gaussian measure of the R iesz transforms of order 1 and the Littlewood-Paley g-function which then i s extended to show the same property for the Riesz transforms of order 2. F or Riesz transforms of higher order boundedness is shown in appropriate spa ces close to L-1.