Weak type $(1,1)$ boundedness of Bochner--Riesz means at the critical index on quantum tori

Abstract: We establish a weak type $(1,1)$ estimate for the Bochner--Riesz mean operator at the critical index $δ=\frac{d-1}{2}$ on the quantum torus $\mathbb{T}<sup>d_θ$, where the associated kernel is rough.