Ruixiang Zhang

collaborators

5 papers

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

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…

math.CA2018

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…

A sharp square function estimate for the cone in R3

Lower bounds for estimates of the Schrödinger maximal function

Sharp L2 estimate of Schrödinger maximal function in higher dimensions

Pointwise convergence of Schrödinger solutions and multilinear refined Strichartz estimates

Weighted restriction estimates and application to Falconer distance set problem

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

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