论文标题
分数Ornstein-uhlenbeck运算符和下层状估计值生成的半群的平滑效应的描述
Description of the smoothing effects of semigroups generated by fractional Ornstein-Uhlenbeck operators and subelliptic estimates
论文作者
论文摘要
我们研究由$ L2（\ Mathbb r^n）$的一般分数Ornstein-Uhlenbeck运营商生成的半群。我们以几何表征这些半群的部分gevrey型平滑性能，并迅速描述了相关的静光的爆炸，在短时间内爆破了相关的静态，从而推广了低纤维化和二次病例。作为这项研究的副产品，我们通过使用插值理论建立了整个空间上分数Ornstein-Uhlenbeck运算符所享有的部分下层次估计值。
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.
