Pseudodifferential operators with non-regular operator-valued symbols

摘要

In this paper, we consider pseudodifferential operators with operator-valued symbols and their mapping properties, without assumptions on the underlying Banach space E. We show that, under suitable parabolicity assumptions, the W_p~k(R~n, E)-realization of the operator generates an analytic semigroup. Our approach is based on oscillatory integrals and kernel estimates for them. An application to non-autonomous pseudodifferential Cauchy problems gives the existence and uniqueness of a classical solution. As an example, we include a discussion of coagulation-fragmentation processes.