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

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.