We introduce Littlewood Paley functions defined in terms of a reparameterization of the Ornstein-Uhlenbeck semigroup obtaining that these operators are bounded in \(L^p\), \(1<p<\infty\), with respect to the unidimensional gaussian measure, by means of singular integrals theory. In addition, we study the Abel summability of the Fourier Hermite expansions considering their pointwise convergence and their convergence in the \(L^p\) sense, obtaining a version of Tauber’s theorem.
