Author

A. Fragkos

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Preprint Nov 2026

Pointwise Ergodic Theorems Along $\lfloor p^c\rfloor$ for Every $c>1$

Let $c>1$ be noninteger, and let $\Lambda$ denote the von Mangoldt function. The averages \[ A_N^{c} f(x):=\frac1N\sum_{n=1}^{N} \Lambda(n)f\bigl(T^{\lfloor n^c\rfloor}x\bigr) \] satisfy the variational estimate \[ \bigl\|\mathcal{V}^r(A_N^{c} f:N\in\mathbb{N})\bigr\|_{L^p(X)} \lesssim_{c,p,r}\|f\|_{L^p(X)} \] for ever...

A. Fragkos · 0 citations

Preprint Sep 2026

Endpoint Estimates for Stein's Purely Quadratic Carleson Operator

We study the near $L^1$ behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_{\lambda} \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 \pi i \lambda y^2} \frac{\mathrm{d} y }{y} \right| \] and its lacunary counterpart obtained by restricting $\lambda$ to $2^{\mathbb{Z}}...

A. Fragkos, Ben Krause, Michael T. Lacey · 0 citations