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 $\delta =\frac{d-1}{2}$ on the quantum torus ${\mathbb{T}}_{\theta }^d$, where the associated kernel is rough.

arXiv comment30 pages