4 papers
Sharp rational points counting near nondegenerate curves in
Shengwen Gan, Shaoming Guo, Changkeun Oh
We establish sharp bounds for rational points near compact smooth nondegenerate curves in , for every . For a nondegenerate curve in …
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|…
Oscillatory integral operators and variable Schrödinger propagators: beyond the universal estimates
Mingfeng Chen, Shengwen Gan, Shaoming Guo +3
We consider a class of Hörmander-type oscillatory integral operators in for odd with real analytic phase. We derive weak conditions on the phase which ens…
The dichotomy of Nikodym sets and local smoothing estimates for wave equations
Mingfeng Chen, Shaoming Guo
We show that Nikodym sets and local smoothing estimates for linear wave equations form a dichotomy: If Nikodym sets for a family of curves exist, then the related maximal operator…