Zusammenfassung
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 ...
Zusammenfassung
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.
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