Analytic semigroups of pseudodifferential operators on vector-valued Sobolev spaces

作者：Barraza Martinez B; Denk R^*; Hernandez Monzon J

来源：Bulletin of the Brazilian Mathematical Society, 2014, 45(2): 197-242.

DOI：10.1007/s00574-014-0046-x

• pseudodifferential operators
• vector-valued Sobolev spaces
• generation of analytic semigroup

In this paper we study continuity and invertibility of pseudodifferential operators with non-regular Banach space valued symbols. The corresponding pseudodifferential operators generate analytic semigroups on the Sobolev spaces W (p) (k) (a%26quot;e (n) , E) with k a a%26quot;center dot(0), 1 a parts per thousand currency sign p a parts per thousand currency sign a. Here E is an arbitrary Banach space. We also apply the theory to solve non-autonomous parabolic pseudodifferential equations in Sobolev spaces.

• 出版日期2014-6