Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup

2006/11/02 by Ebner Pineda, Pineda, Ebner, Wilfredo Urbina +1
Mathematics · #26A99 #42C10 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.math/0611040

openalex publication_date 2006/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are going to get the non tangential convergence, in an appropriated parabolic "gaussian cone", of the Ornstein-Uhlenbeck semigroup in providing two proofs of this fact. One is a direct proof by using the truncated non tangential maximal function associated. The second one is obtained by using a general statement. This second proof also allows us to get a similar result for the Poisson-Hermite semigroup.

Related

• A note on the Gaussian maximal functions
• Parabolic type semigroups: asymptotics and order of contact
• On a nonsymmetric Ornstein-Uhlenbeck semigroup and its generator
• Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
• The Boundedness of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure