Endpoint Estimates for Stein's Purely Quadratic Carleson Operator

Anastasios Fragkos, Ben Krause, Michael Lacey

We study the near $L^1$ behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_λ \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 πi…