论文标题
一般高斯环境中的光谱乘数
Spectral multipliers in a general Gaussian setting
论文作者
论文摘要
我们研究了Ornstein-uhlenbeck运算符$ \ Mathcal l $ in $ \ Mathbb r^n $中的一类光谱乘数，其特征值的真实零件是负面的。我们证明，如果$ m $是右半平面定义的拉普拉斯变换类型的函数，则相对于$ \ mathbb r^n $的不变度度量，$ m（\ mathcal l）$是弱类型$（1，1）$。证明涉及相关积分内核的许多估计，也涉及梅勒内核的时间衍生物的数量，以及Ornstein-uhlenbeck最大运算符定理的增强版本。
We investigate a class of spectral multipliers for an Ornstein-Uhlenbeck operator $\mathcal L$ in $\mathbb R^n$, with drift given by a real matrix $B$ whose eigenvalues have negative real parts. We prove that if $m$ is a function of Laplace transform type defined in the right half-plane, then $m(\mathcal L)$ is of weak type $(1, 1)$ with respect to the invariant measure in $\mathbb R^n$. The proof involves many estimates of the relevant integral kernels and also a bound for the number of zeros of the time derivative of the Mehler kernel, as well as an enhanced version of the Ornstein-Uhlenbeck maximal operator theorem.
