Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}. $$ We prove that, ...

We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proof is inspired by ones by Bourgain and ...

The Bochner–Riesz multipliers are shown to satisfy a range of sparse bounds. The range of sparse bounds increases to the optimal range, as δ increases to the critical value, even assuming only partial information on the ...