ON THE ORNSTEIN UHLENBECK OPERATOR PERTURBED BY SINGULAR POTENTIALS IN L~p-SPACES

摘要

In this paper we give sufficient conditions ensuring that the space of test functions C_c~∞(R~N) is a core for the operator L_0u = △u - Mx · ▽u + α/|x|2u =: Lu + α/|x|2u, and L_o with domain W_μ~(2,p){R~N) generates a quasi-contractive and positiv-ity preserving Co-semigroup in L_μ~P(R~N), 1 ＜ p ＜ ∞. Here M is a positive definite N × N hermitian matrix and μ, is the unique invariant measure for the Ornstein-Uhlenbeck operator L. The proofs are based on an L~p-weighted Hardy's inequality and perturbation techniques.