A characterization of the Gaussian Lipschitz space and sharp estimates for the Ornstein-Uhlenbeck Poisson kernel

Journal article, 2016

In the n-dimensional Ornstein-Uhlenbeck setting, a Lipschitz space was defined by Gatto and Urbina, in terms of the gradient of the Ornstein-Uhlenbeck Poisson integral of the function. We show that this space can also be described as a Lipschitz space in the ordinary sense, by means of an inequality for the modulus of continuity. The proof is based on several estimates for the Ornstein-Uhlenbeck Poisson kernel and its gradient, also of independent interest.