Communications of the
Korean Mathematical Society CKMS

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials \begin{align*} A_{\Phi,G,V,c} = \Delta-\nabla \Phi\cdot\nabla+G\cdot \nabla-V+c|x|^{-2} \end{align*} with a suitable domain generates a quasi-contractive, positive and analytic $C_{0}$-semigroup in $L^{p}(\mathbb{R}^{N},e^{-\Phi(x)}dx)$, $1

Keywords: Inverse square potential, regular potential, weighted Hardy inequality, generalized Ornstein-Uhlenbeck operator, $C_{0}$-semigroup, perturbation theory

MSC numbers: Primary 47D60, 47D06, 35K15