On Gaussian Lipschitz spaces and the boundedness of Fractional Integrals and Fractional Derivatives on them

Abstract

In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs of the ones given in the classical case and moreover can be extended to the case of Laguerre and Jacobi expansions too