JournalsrmiVol. 32, No. 4pp. 1189–1210

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

  • Liguang Liu

    Renmin University of China, Beijing, China

  • Peter Sjögren

    Chalmers University of Technology, Göteborg, Sweden
A characterization of the Gaussian Lipschitz space and sharp estimates for the Ornstein–Uhlenbeck Poisson kernel cover
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Abstract

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.

Cite this article

Liguang Liu, Peter Sjögren, A characterization of the Gaussian Lipschitz space and sharp estimates for the Ornstein–Uhlenbeck Poisson kernel. Rev. Mat. Iberoam. 32 (2016), no. 4, pp. 1189–1210

DOI 10.4171/RMI/912