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arXiv · 2502.16248

Fourier-Wigner multipliers and the Bochner-Riesz conjecture for Schatten class operators

Helge Jørgen Samuelsen
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Abstract

In this paper we introduce the notion of Fourier-Wigner multipliers for the Schatten class operators $\mathcal{S}^p$, which acts as an extension of classical localisation operators in time-frequency analysis. We establish results about Fourier-Wigner multipliers through convolution with rank-one operators and Werner-Young's inequality. We are also able to prove an equivalence relation for compactly supported Fourier multipliers. This allows us to reformulate the Bochner-Riesz conjecture in terms of Schatten class operators.

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Helge Jørgen Samuelsen. 2025-02-22. Fourier-Wigner multipliers and the Bochner-Riesz conjecture for Schatten class operators. https://arxiv.org/abs/2502.16248

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