Xiumin Du

collaborators

Showing math.CAShow all

3 papers · 1 filter

math.CA2026

The divergence set for the wave equation in higher dimensions

Xiumin Du, Terence L. J. Harris, Jianhui Li

It is shown that if $u$ solves the wave equation in $R^{4 + 1}$ with initial data $u (\cdot, 0) = u_{0} (\cdot) \in H^{s}$ and $\partial_{t} u (\cdot, 0) = u_{1} (\cdot) \in H^{s - 1}$ , whe…

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.CA2024

$L^{p}$ estimates of the maximal Schrödinger operator in $R^{n}$

Xiumin Du, Jianhui Li

We obtain $L^{p}$ estimates of the maximal Schrödinger operator in $R^{n}$ using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estima…

The divergence set for the wave equation in higher dimensions

Lp weighted Fourier restriction estimates

Lp estimates of the maximal Schrödinger operator in Rn

$L^{p}$ weighted Fourier restriction estimates

$L^{p}$ estimates of the maximal Schrödinger operator in $R^{n}$