Revista Matemática Iberoamericana


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Volume 32, Issue 4, 2016, pp. 1189–1210
DOI: 10.4171/RMI/912

Published online: 2016-12-16

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

Liguang Liu[1] and Peter Sjögren[2]

(1) Renmin University of China, Beijing, China
(2) Chalmers University of Technology, Göteborg, Sweden

The Gaussian Lipschitz space was defined by Gatto and Urbina, by means of the Ornstein–Uhlenbeck Poisson kernel. We give a characterization of this space in terms of a combination of ordinary Lipschitz continuity conditions. The main tools used in the proof are sharp estimates of the Ornstein–Uhlenbeck Poisson kernel and some of its derivatives.

Keywords: Gauss measure space, Lipschitz space, Ornstein–Uhlenbeck Poisson kernel

Liu Liguang, Sjögren Peter: A characterization of the Gaussian Lipschitz space and sharp estimates for the Ornstein–Uhlenbeck Poisson kernel. Rev. Mat. Iberoamericana 32 (2016), 1189-1210. doi: 10.4171/RMI/912