6 papers
A Hard-Analytic Proof of "Most" Polynomial Wiener-Wintner Theorems for Infinite Measure Spaces
Ben Krause
We provide a new proof of ``most" cases of the polynomial Wiener-Wintner theorem for -finite spaces, using hard-analytic methods. Specifically, we prove that whenever …
On Multi-linear Maximal Operators Along Homogeneous Curves
Lars Becker, Ben Krause
Suppose that \[ \vecγ(t) := (γ_1(t),\dots,γ_n(t)) = (a_1 t^{d_1},\dots,a_n t^{d_n}), \; \; \; 1\leq d_1 < \dots < d_n, \ a_i \neq 0\] is a homogeneous polynomial curve. We prove th…
On Polynomial Progressions Inside Sets of Large Dimension
Ben Krause, Ana de Orellana
In this note we connect Sobolev estimates in the context of polynomial averages e.g.\ \begin{align}\label{e:savings} \| \int_0^1 \prod_{k=1}^m f_k(x-t^k) \|_{1} \leq \text{Const} \…
Quantitative Convergence for Sparse Ergodic Averages in
Ben Krause, Yu-Chen Sun
We provide a unified framework to proving pointwise convergence of sparse sequences, deterministic and random, at the endpoint. Specifically, suppose that \[ a_n \in \{ \l…
Multi-Frequency Oscillation Estimates Arising in Pointwise Ergodic Theory
Ben Krause
We prove essentially optimal -estimates for variational variants of the maximal Fourier multiplier operators considered by Bourgain in his work on pointwise conver…
A Unified Approach to Two Pointwise Ergodic Theorems: Double Recurrence and Return Times
Ben Krause
We present a unified approach to extensions of Bourgain's Double Recurrence Theorem and Bourgain's Return Times Theorem to integer parts of the Kronecker sequence, emphasizing stop…