Analytic semigroups of pseudodifferential operators on vector-valued Sobolev spaces
B. Barraza Martínez, R. Denk, and J. Hernández Monzón
Abstract. 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 in E-valued Lp-Sobolev spaces where E is an arbitrary Banach space. We also apply the theory to solve non-autonomous parabolic pseudodifferential equations in Sobolev spaces.
Bull. Braz. Math. Soc. (N.S.) 45 (2014), 197-242.
The paper is available here (Preprint version).
Springer Link: http://link.springer.com/article/10.1007/s00574-014-0046-x