Decoupling for Schatten class operators in the setting of quantum harmonic analysis

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-11-08 DOI:10.1112/blms.13178

Helge J. Samuelsen

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引用次数: 0

Abstract

We introduce the notion of decoupling for operators, and prove an equivalence between classical $ℓ^{q} L^{p}$ decoupling for functions and $ℓ^{q} S^{p}$ decoupling for operators on bounded sets in $R^{2 d}$ . We also show that the equivalence depends only on the bounded set $Ω$ and not on the values of $p, q$ nor on the partition of $Ω$ . The proof relies on a quantum version of Wiener's division lemma.