Description of the smoothing effects of semigroups generated by fractional Ornstein-Uhlenbeck operators and subelliptic estimates

2020/07/09 by Paul Alphonse, Alphonse, Paul
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.2007.04593

openalex publication_date 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study semigroups generated by general fractional Ornstein-Uhlenbeck operators acting on L2(\mathbb Rⁿ). We characterize geometrically the partial Gevrey-type smoothing properties of these semigroups and we sharply describe the blow-up of the associated seminorms for short times, generalizing the hypoelliptic and the quadratic cases. As a byproduct of this study, we establish partial subelliptic estimates enjoyed by fractional Ornstein-Uhlenbeck operators on the whole space by using interpolation theory.

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