ON THE GENERALIZED ORNSTEIN-UHLENBECK OPERATORS WITH REGULAR AND SINGULAR POTENTIALS IN WEIGHTED LP-SPACES

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials A(phi,G,V,c)= Delta -del phi center dot del+G center dot del -V+c|x|(-2) with a suitable domain generates a quasi -contractive, positive and analytic C-0-semigroup in L-p(R-N, e(-phi(x))dx), 1 < p < infinity. The proofs are based on an L-p-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].