Some results on Gaussian Besov-Lipschitz spaces and Gaussian Triebel-Lizorkin spaces

In this paper we consider the Gaussian Besov-Lipschitz B α p,q (γ d) and Gaussian Triebel-Lizorkin F α p,q (γ d) spaces, for any α > 0, studying the inclusion relations among them, proving that the Gaussian Sobolev spaces L p α (γ d) are contained in them, giving some interpolation results and studying the continuity properties of the Ornstein-Uhlenbeck semigroup, the Poisson-Hermite semigroup and the Bessel potentials on them.