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arXiv · 2412.05879

Bounds on pseudodifferential operators and Fourier restriction for Schatten classes

Detlef Müller
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Abstract

As main result, we show that a pseudodifferential operator in the Weyl calculus, whose symbol has compact Fourier support, lies in the Schatten class $\mathcal S^p$ if and only if its symbol lies in the Lebesgue space $L^p$ on phase space. As an immediate consequence, this gives an alternative and very lucid proof of a recent result by Luef and Samuelsen, who had discovered that for compactly supported measures $\mu,$ classical Fourier restriction estimates with respect to the measure $\mu$ are equivalent to quantum restriction estimates for the Fourier-Wigner transform for Schatten classes.

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Detlef Müller. 2024-12-08. Bounds on pseudodifferential operators and Fourier restriction for Schatten classes. https://arxiv.org/abs/2412.05879

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