Ruixiang Zhang

activity

20132024

most citedWeighted restriction estimates and application to Falconer distance set problem

33 citations · 68 across the 11 of their papers we have counts for

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10 papers · 1 filter

math.CA2024

$L^{p}$ weighted Fourier restriction estimates

Xiumin Du, Jianhui Li, Hong Wang +1

We obtain some sharp $L^{p}$ weighted Fourier restriction estimates of the form $∥ E f ∥_{L^{p} (B^{n + 1} (0, R), H d x)} ⪅ R^{β} ∥ f ∥_{2}$ , where $E$ is the Fourier extension operator o…

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.CA2019

A sharp square function estimate for the cone in $R^{3}$

Larry Guth, Hong Wang, Ruixiang Zhang

We prove a sharp square function estimate for the cone in $R^{3}$ and consequently the local smoothing conjecture for the wave equation in $2 + 1$ dimensions.

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…

Lp weighted Fourier restriction estimates