Quantum Bochner–Riesz conjecture

Let $d$ be a positive integer, let $m_\delta$ be the Bochner–Riesz multiplier from the classical formulation, and let $\mathfrak{M}_p({\mathbb R}^{2d})$ denote the class of multipliers whose Fourier-Wigner multiplier operators extend boundedly on the Schatten class ${\mathcal S}^p$. Quantum Bochner–Riesz conjecture. For $\delta>0$, the multiplier $m_\delta$ belongs to $\mathfrak{M}_p({\mathbb R}^{2d})$ if and only if

$$\left|\frac{1}{p}-\frac{1}{2}\right|<\frac{2\delta+1}{4d}.$$

Because compactly supported classical and Fourier-Wigner multiplier classes are identified by the preceding theorem, this is the Fourier-Wigner, or quantum, reformulation of the Bochner–Riesz conjecture. The source does not report a resolution, so the conjecture is recorded as open.