Georgia Institute of Technology College of Sciences

We will describe sufficient conditions on a set $\Lambda \subset [0,2\pi) $ so that the maximal operator below is bound on $\ell^2(Z)$. $$\sup _{\lambda \in \Lambda} \Big| \sum_{n\neq 0} e^{i \lambda n^2} f(x-n)/n\Big|$$ The integral version of this result is an influential result to E.M. Stein. Of course one should be able to take $\Lambda = [0,2\pi) $, but such a proof would have to go far beyond the already complicated one we will describe. Joint work with Ben Krause.