Functional analysis in cone and edge Sobolev spaces

✍ Scribed by Tankred Hirschmann

• Book ID: 104632837
• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 926 KB
• Volume: 8
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00128002

✦ Synopsis

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 aspectsof this approach introducing so-called abstract F-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 regular F-transforms.