Leonidas Daskalakis

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20222026

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math.DS2024

Pointwise ergodic theorems along fractional powers of primes

Erik Bahnson, Leonidas Daskalakis, Abbas Dohadwala +1

We establish pointwise convergence for nonconventional ergodic averages taken along $⌊ p^{c} ⌋$ , where $p$ is a prime number and $c \in (1, 4/3)$ on $L^{r}$ , $r \in (1, \infty)$ .…

math.DS2024

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…