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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…
math.CA2025
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…
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…