6 papers
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…
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 $(X,μ,T)…
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…
On Polynomial Progressions Inside Sets of Large Dimension
Ben Krause
In this note we connect Sobolev estimates in the context of polynomial averages e.g. \[ \| \int_0^1 \prod_{k=1}^m f_k(x-t^k) \|_{1} \leq \text{Const} \cdot 2^{-\text{const} \cdot 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…