A direct approach to generation of analytic semigroups by generalized Ornstein–Uhlenbeck operators in weighted spaces.

Abstract: Generation of analytic semigroups by generalized Ornstein–Uhlenbeck operators in the weighted space is shown. The results improve the recent results established by Metafune–Prüss–Rhandi–Schnaubelt (2005) [8] ( ) and Kojima–Yokota (2010) [6] ( ). The proofs of those are based on a generation result acting on the unweighted space [8, Theorem 3.4], while ours is carried out by an application of -theory for second-order elliptic operators [13, Theorem 1.3] obtained by Sobajima (2012). Consequently, the additional condition assumed in both [8,6] is completely removed. [Copyright &y& Elsevier]