A Discrete Quadratic Carleson Theorem

Analysis Seminar
Wednesday, February 3, 2016 - 2:00pm
1 hour (actually 50 minutes)
Skiles 005
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.