Xiumin Du

activity

20182023

most citedWeighted refined decoupling estimates and application to Falconer distance set problem

1 citations · 1 across the 2 of their papers we have counts for

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math.CA2023★ 1 cited

Weighted refined decoupling estimates and application to Falconer distance set problem

Xiumin Du, Yumeng Ou, Kevin Ren +1

We prove some weighted refined decoupling estimates. As an application, we give an alternative proof of the following result on Falconer's distance set problem by the authors in a…

math.CA2023

New improvement to Falconer distance set problem in higher dimensions

Xiumin Du, Yumeng Ou, Kevin Ren +1

We show that if a compact set $E \subset R^{d}$ has Hausdorff dimension larger than $\frac{d}{2} + \frac{1}{4} - \frac{1}{8 d + 4}$ , where $d \geq 3$ , then there is a point $x \in E$ …

math.CA2023

On a free Schrödinger solution studied by Barceló--Bennett--Carbery--Ruiz--Vilela

Xiumin Du, Yumeng Ou, Hong Wang +1

We present a free Schrödinger solution studied by Barceló--Bennett--Carbery--Ruiz--Vilela and show why it can be viewed as a sharp example for the recently discovered refined decou…

math.CA2020

An improved result for Falconer's distance set problem in even dimensions

Xiumin Du, Alex Iosevich, Yumeng Ou +2

We show that if compact set $E \subset R^{d}$ has Hausdorff dimension larger than $\frac{d}{2} + \frac{1}{4}$ , where $d \geq 4$ is an even integer, then the distance set of $E$ …

math.CA2019

Upper bounds for Fourier decay rates of fractal measures

Xiumin Du

For spherical and parabolic averages of the Fourier transform of fractal measures, we obtain new upper bounds on rates of decay by an "intermediate dimension" trick.

math.CA2019

Lower bounds for estimates of the Schrödinger maximal function

Xiumin Du, Jongchon Kim, Hong Wang +1

We give new lower bounds for $L^{p}$ estimates of the Schrödinger maximal function by generalizing an example of Bourgain.