论文标题
Riesz变换了一般的Ornstein-Uhlenbeck Semigroup
Riesz transforms of a general Ornstein--Uhlenbeck semigroup
论文作者
论文摘要
我们考虑了与Ornstein相关的任何订单的Riesz转换 - uhlenbeck操作员$ \ MATHCAL L $，并带有协方差$ Q $，由真实，对称和积极的确定矩阵给出，并且由真实矩阵给出的漂移$ b $，其特征值具有负面的真实零件。在这种一般的高斯语境中，我们证明，相对于不变的度量，当且仅当它的订单最多为$ 2 $时，Riesz变换是薄弱的$（1,1）$。
We consider Riesz transforms of any order associated to an Ornstein--Uhlenbeck operator $\mathcal L$, with covariance $Q$ given by a real, symmetric and positive definite matrix, and with drift $B$ given by a real matrix whose eigenvalues have negative real parts. In this general Gaussian context, we prove that a Riesz transform is of weak type $(1,1)$ with respect to the invariant measure if and only if its order is at most $2$.
