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

IF 0.9 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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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.

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量子谐波分析下Schatten类算子的解耦

我们引入算子解耦的概念，并证明了函数的经典的lqlp $\ell ^qL^p$解耦与lq之间的等价S p$ \ well ^q{\mathcal {S}}^p$解耦在r2中有界集合上的算子${\mathbb {R}}^{2d}$。我们还证明了等价性只依赖于有界集合Ω $\Omega$，而不依赖于p，q$ p,q$的值，也不依赖于Ω $\Omega$的划分。这个证明依赖于维纳除法引理的量子版本。

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