Functional analysis in cone and edge Sobolev spaces

In the pseudodifferential calculus on manifolds with singularities there appear operator-valued pseudodifferential operators in terms of the Fourier and Mellin transform. This gives rise to generalize some aspects of this approach introducing so-called abstractF-transforms. We describe the basic pseudodifferential calculus and Sobolev spaces with respect to such transforms. We prove interpolation properties of these Sobolev spaces and a characterization of regularF-transforms.