论文标题
在某些与非脱位对称$α$稳定的可能性指标相关的操作员上
On Some Operators Associated with Non-Degenerate Symmetric $α$-Stable Probability Measures
论文作者
论文摘要
与非分类对称$α$稳定的运算符的有界性能，（1,2）$ in（1,2）$，$ \ Mathbb {r}^d $的概率度量进行了调查，以适当的欧几里得或其他方式进行，$ l^p $ - spaces，$ spaces，$ p \ in（$ p \ in（1，1，++\ infty）$。我们的方法是基于首先获得Bismut型公式，这为各种运营商提供了有用的表示。在欧几里得的环境中，转移方法和一维乘数理论结合稳定分布的精细特性提供了分数laplacian的无维估计。在非欧亚人环境中，当参考度量是旋转不变的$α$稳定的可能性度量时，我们获得了非偏差情况的有界性结果以及无维度的估计。
Boundedness properties of operators associated with non-degenerate symmetric $α$-stable, $α\in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in (1,+\infty)$. Our approach is based on first obtaining Bismut-type formulae which lead to useful representations for various operators. In the Euclidean setting, the method of transference and one-dimensional multiplier theory combined with fine properties of stable distributions provide dimension-free estimates for the fractional Laplacian. In the non-Euclidean setting, we obtain boundedness results for the non-singular cases as well as dimension-free estimates when the reference measure is the rotationally invariant $α$-stable probability measure.
