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.

Author

Liguang Liu

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Revista Matematica Iberoamericana

0213-2230 (ISSN)

Vol. 32 4 1189--1210-

Roots

Basic sciences

Subject Categories

Mathematical Analysis

DOI

10.4171/RMI/912

More information

Created

10/8/2017