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

• Liguang Liu ^[1] ; Peter Sjögren ^[2]
  1. [1] Renmin University of China

     Renmin University of China

     China

     
  2. [2] University of Gothenburg

     University of Gothenburg

     Suecia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 4, 2016, págs. 1189-1210
• Idioma: inglés
• DOI: 10.4171/RMI/912
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.