8 papers
Pointwise ergodic theorems along sequences of intermediate growth
Leonidas Daskalakis, Mariusz Mirek, Máté Wierdl
We establish the first pointwise convergence result for ergodic averages with iterates along explicit and deterministic sequences of intermediate growth, that is, growing faster th…
Pointwise convergence of ergodic averages along quadratic bracket polynomials
Leonidas Daskalakis
We establish a pointwise convergence result for ergodic averages modeled along orbits of the form , where is an arbitrary positive…
Ergodic theorems for bilinear averages, Roth's Theorem and Corners along fractional powers
Leonidas Daskalakis
We prove that for every , every probability space equipped with two commuting measure-preserving transformations and every $f,…
Pointwise ergodic theorems for non-conventional bilinear averages along
Leonidas Daskalakis
For every and every probability dynamical system we prove that for any the bilinear ergodic averages \[ \frac{1}{N}\s…
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 , where is a prime number and on , .…
Fractionally modulated discrete Carleson's Theorem and pointwise Ergodic Theorems along certain curves
Leonidas Daskalakis, Anastasios Fragkos
For 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…
Weak-type (1,1) inequality for discrete maximal functions and pointwise ergodic theorems along thin arithmetic sets
Leonidas Daskalakis
We establish weak-type bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin deterministic sets . As a corollary we…
Roth's Theorem and the Hardy--Littlewood majorant problem for thin subsets of primes
Leonidas Daskalakis
We introduce a wide class of deterministic subsets of primes of zero relative density and we prove Roth's Theorem in these sets, namely, we show that any subset of them with positi…