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

Abstract

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.