Riesz Potentials, Bessel Potentials and Fractional Derivatives on Besov-Lipschtz spaces for the Gaussian Measure

Abstract

In this paper we will study the boundedness of Riesz Potentials, Bessel potentials and Fractional Derivatives on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\alpha }({\gamma }_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.