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

Liguang Liu ; Peter Sjögren (Institutionen för matematiska vetenskaper)
Revista matemática iberoamericana (0213-2230). Vol. 32 (2016), 4, p. 1189--1210.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2014-09-10. Senast ändrad 2016-12-13.
CPL Pubid: 202556

 

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