2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61497Carleson's theorem on the pointwise convergence of Fourier series provides bounds for a maximal operator, with the maximum taken over all choices of linear functions of a phase argument. We extend this to all quadratic choices of phase functions. Specifically, we show that the maximal operator below maps $L^p$ into itself for $1<p<\infty$. $$ \sup_a \sup_b |\int e^{i(ay^2+by)}f(x-y)dy/y| $$Classical Analysis and ODEs42text