Fractionally modulated discrete Carleson's Theorem and pointwise Ergodic Theorems along certain curves

Leonidas Daskalakis, Anastasios Fragkos

For $c\in (1,2)$ we consider the following operators \[ \mathcal{C}_{c}f(x) = \sup_{λ\in [-1/2,1/2)}\bigg| \sum_{n \neq 0}f(x-n) \frac{e^{2πiλ\lfloor |n|^{c} \rfloor}}{n}\bigg|\text…