Showing math.CAShow all
2 papers · 1 filter
math.CA2025
A counterexample for local smoothing for averages over curves
David Beltran, Jonathan Hickman
We provide a new necessary condition for local smoothing estimates for the averaging operator defined by convolution with a measure supported on a smooth non-degenerate curve in $\…
math.CA2024
On a planar Pierce--Yung operator
David Beltran, Shaoming Guo, Jonathan Hickman
We show that the operator \begin{equation*} \mathcal{C} f(x,y) := \sup_{v\in \mathbb{R}} \Big|\mathrm{p.v.} \int_{\mathbb{R}} f(x-t, y-t^2) e^{i v t^3} \frac{\mathrm{d} t}{t} \Big|…