A. Fragkos

Endpoint Estimates for Stein's Purely Quadratic Carleson Operator

We study the near $L^1$ behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_{\lambda} \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 \pi i \lambda y^2} \frac{\mathrm{d} y }{y} \right| \] and its lacunary counterpart obtained by restricting $\lambda$ to $2^{\mathbb{Z}}...