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, Vol. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 00018708
• Language: English