A direct approach to generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators in weighted L-p spaces

作者：Sobajima Motohiro; Yokota Tomomi^*

来源：Journal of Mathematical Analysis and Applications, 2013, 403(2): 606-618.

DOI：10.1016/j.jmaa.2013.02.054

• Ornstein-Uhlenbeck operator
• Analytic semigroup

Generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators A = -Delta + del Phi . del - G . del + V in the weighted space L-p(R-N, e(-Phi(x))dx) is shown. The results improve the recent results established by Metafune-Priiss-Rhandi-Schnaubelt (2005) [8] (V equivalent to 0) and Kojima-Yokota (2010) [6] (V not equivalent to 0). The proofs of those are based on a generation result acting on the unweighted space L-p(R-N) [8, Theorem 3.41, while ours is carried out by an application of L-p-theory for second-order elliptic operators [13, Theorem 1.31 obtained by Sobajima (2012). Consequently, the additional condition vertical bar divG vertical bar %26lt;= epsilon(vertical bar del Phi vertical bar(2) + V) + C-epsilon assumed in both [8,6] is completely removed.

• 出版日期2013-7-15