Xiumin Du

activity

20152023

most citedWeighted restriction estimates and application to Falconer distance set problem

33 citations · 87 across the 14 of their papers we have counts for

collaborators

14 papers

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.CA2021

On the multiparameter Falconer distance problem

Xiumin Du, Yumeng Ou, Ruixiang Zhang

We study an extension of the Falconer distance problem in the multiparameter setting. Given $ℓ \geq 1$ and $R^{d} = R^{d_{1}} \times \dots \times R^{d_{ℓ}}$ …

math.CA2020★ 8 cited

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.AP2020

Counterexamples to $L^{p}$ collapsing estimates

Xiumin Du, Matei Machedon

We show that certain $L^{2}$ space-time estimates for generalized density matrices which have been used by several authors in recent years to study equations of BBGKY or Hartree-Fock…

math.CA2019★ 10 cited

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★ 11 cited

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.

math.CA2018★ 8 cited

Sharp $L^{2}$ estimate of Schrödinger maximal function in higher dimensions

Xiumin Du, Ruixiang Zhang

We show that, for $n \geq 3$ , $lim_{t \to 0} e^{i t Δ} f (x) = f (x)$ holds almost everywhere for all $f \in H^{s} (R^{n})$ provided that $s > \frac{n}{2 ( n + 1 )}$ . Due to a counterexam…

math.CA2018★ 5 cited

Pointwise convergence of Schrödinger solutions and multilinear refined Strichartz estimates

Xiumin Du, Larry Guth, Xiaochun Li +1

We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geq…

math.CA2018★ 33 cited

Weighted restriction estimates and application to Falconer distance set problem

Xiumin Du, Larry Guth, Yumeng Ou +3

We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates…

math.CA2016★ 6 cited

A sharp Schrodinger maximal estimate in $R^{2}$

Xiumin Du, Larry Guth, Xiaochun Li

We show that $lim_{t \to 0} e^{i t Δ} f (x) = f (x)$ almost everywhere for all $f \in H^{s} (R^{2})$ provided that $s > 1/3$ . This result is sharp up to the endpoint. The proof uses…

math.CA2016

$l^{p}$ decoupling for restricted $k$ -broadness

Xiumin Du, Xiaochun Li

To prove Fourier restriction estimate using polynomial partitioning, Guth introduced the concept of $k$ -broad part of regular $L^{p}$ norm and obtained sharp $k$ -broad restriction es…

math.CA2015★ 5 cited

$L^{p}$ -estimates of maximal function related to Schrödinger Equation in $R^{2}$