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math.CA2025
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…
math.CA2025
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} \…
math.CA2025
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…