Riesz Potentials, Bessel Potentials and Fractional Derivatives on   Triebel-Lizorkin spaces for the Gaussian Measure
  In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\alpha}(\gamma_d)$. In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces $F_{p,q}^{\alpha}(\gamma_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups. 
A. Eduardo Gatto, Ebner Pineda, Wilfredo Urbina
math.CA