A counter example on nontangential convergence for oscillatory integrals

半线性热方程的振荡爆破与梯度估计

Oscillatory blow-up and gradient estimates for semilinear heat equations

针对半线性热方程爆破理论的基础问题，构造了任意超临界幂次下具有振荡L^∞范数的非径向爆破反例，扩展了II型爆破的幂次范围并明确了梯度估计的适用时刻。

满足齐次Carleson-Sjölin型条件的振荡积分算子的平方函数不等式

Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions

本文通过建立改进的变系数平方函数不等式，利用多重线性振荡积分估计和分解不等式，改进了满足电影曲率条件的傅里叶积分算子的局部光滑估计，尤其对$2<p\leq 3$得到几乎尖锐结果，并推进了$p=4$的估计，进而改进了流形上波动方程的局部光滑估计。

Sharp local smoothing estimates for Fourier integral operators

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local smoothing estimates for a natural class of Fourier integral operators. We also show how local smoothing estimates imply oscillatory integral estimates and obtain a maximal variant of an oscillatory integral estimate of Stein. Together with an oscillatory integral counterexample of Bourgain, this shows that our local smoothing estimates are sharp in odd spati…