Abels, Helmut and Pfeuffer, Christine (2018) Characterization of Non-Smooth Pseudodifferential Operators. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 24 (2). pp. 371-415. ISSN 1069-5869, 1531-5851
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Smooth pseudodifferential operators on can be characterized by their mapping properties between Sobolev spaces due to Beals and Ueberberg. In applications such a characterization would also be useful in the non-smooth case, for example to show the regularity of solutions of a partial differential equation. Therefore, we will show that every linear operator P, which satisfies some specific continuity assumptions, is a non-smooth pseudodifferential operator of the symbol-class . The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRAL-INVARIANCE; ALGEBRAS; Non-smooth pseudodifferential operators; Characterization by mapping properties; Commutator estimates |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 Mar 2020 09:07 |
| Last Modified: | 19 Mar 2020 09:07 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14863 |
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