Endpoint Schatten class properties of commutators

Frank, Rupert L. ; Sukochev, Fedor und Zanin, Dmitriy (2024): Endpoint Schatten class properties of commutators. In: Advances in Mathematics, Bd. 450, 109738

Abstract

We study the trace ideal properties of the commutators of a power of the Laplacian with the multiplication operator by a function f on R[superscript]d. For a certain range of [little] E E[lement of] R, we show that this commutator belongs to the weak Schatten class [] if and only if the distributional gradient of f belongs to [] . Moreover, in this case we determine the asymptotics of the singular values. Our proofs use, among other things, the tool of Double Operator Integrals.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 00018708
• Sprache: Englisch