Xiumin Du

activity

20182020

collaborators

7 papers

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.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

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.

math.CA2018

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

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…