Riesz potentials, Bessel potentials and fractional derivatives on Triebel-Lizorkin spaces for the Gaussian measure

In [3] the boundedness properties of Riesz potentials, Bessel potentials and fractional derivatives were studied in detail on Gaussian Besov-Lipschitz spaces Bp,qα(γd). In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces Fp,qα(γd). Also, these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.