Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

Ben Krause, Joris Roos

Consider the maximal operator $$\mathscr{C} f(x) = \sup_{λ\in\mathbb{R}}\Big|\sum_{\substack{y\in\mathbb{Z}^n\setminus\{0\}}} f(x-y) e(λ|y|^{2d}) K(y)\Big|,\quad (x\in\mathbb{Z}^n)…