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• #### Sparse bounds for the discrete spherical maximal functions ﻿

(2020)
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 ...
• #### Uniform sparse bounds for discrete quadratic phase Hilbert transforms ﻿

(2017-09)
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, ...