Michael Lacey

Title:  A Discrete version of a quadratic Carleson theorem.  

Abstract:  We give sufficient conditions on $ \Lambda $ under which the discrete maximal function below is bounded on $ \ell ^2(\mathbb{Z})$.
$$
\mathcal{C}_{\Lambda} f( n ) := \sup_{ \lambda \in \Lambda} \biggl\lvert  \sum_{m \neq 0} f(n-m) \frac{ e ^{2 \pi i\lambda m^2}}  {m} \biggr\rvert
$$ 
The set $\Lambda $ can be certain kinds of Cantor sets, for instance. The integral version of this result holds with no restriction on $\Lambda$, and is due to E. M. Stein's. Joint work with Ben Krause. 

 

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