Pseudodifferential operators with non-regular operator-valued symbols
B. Barraza Martínez, R. Denk, and J. Hernández Monzón
Abstract. In this paper, we consider pseudodifferential operators with operator-valued symbols and their mapping properties, without assumptions on the underlying Banach space. We show that, under suitable parabolicity assumptions, the realization of the operator in the standard Sobolev space generates an analytic semigroup. An application to non-autonomous pseudodifferential Cauchy problems gives the existence and uniqueness of a classical solution. Our approach is based on oscillatory integrals and kernel estimates for them.
Manuscripta Math.144 (2014), 349-372.
DOI 10.1007/s00229
The paper is available here (Preprint version).