Generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators with potentials

It is shown that the generalized Ornstein-Uhlenbeck operator “with potential” AΦ,G,Vu:=Δu−∇Φ⋅∇u+G⋅∇u−Vu with suitable domain generates an analytic semigroup on the weighted space Lp(RN,μ), 1<p<∞, where . The result extends the generation theorem established by Metafune-Prüss-Rhandi-Schnaubelt when V≡0 to the case where V?0, while the proof is based on their useful theorem that a class of second order elliptic operators generates an analytic semigroup on the unweighted space Lp(RN).