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arXiv · 2007.04593

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

Paul Alphonse
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Abstract

We study semigroups generated by general fractional Ornstein-Uhlenbeck operators acting on $L2(\mathbb R^n)$. 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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Paul Alphonse. 2020-07-09. Description of the smoothing effects of semigroups generated by fractional Ornstein-Uhlenbeck operators and subelliptic estimates. https://arxiv.org/abs/2007.04593

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