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 on the Sobolev spaces W (ℝ n , E) with k ∈ ℕ0, 1 ≤ p ≤ ∞. Here E is an arbitrary Banach space. We also apply the theory to solve non-autonomous parabolic pseudodifferential equations in Sobolev spaces.
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