Abstract
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.
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Communicated by B. W. Schulze
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Hirschmann, T. Functional analysis in cone and edge Sobolev spaces. Ann Glob Anal Geom 8, 167–192 (1990). https://doi.org/10.1007/BF00128002
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DOI: https://doi.org/10.1007/BF00128002