论文标题
平滑度有限的均匀固定相估计
Uniform stationary phase estimate with limited smoothness
论文作者
论文摘要
在本文中，我们考虑了与固定相的振荡积分的均匀估计值，而Alazard-Burq-Zuily先前研究了固定相。对于均匀估计，我们大大降低了相位所需的规律性条件的顺序和振幅功能。我们还研究了哪个相和振幅函数依赖振荡参数的振荡积分的估计值。本文的新颖性在于使用波数据包分解，这将振动估算值转化为波数据包支持的偏置性能的振荡估计。后者本质上是几何形状，对相位和振幅功能的平滑度不太敏感。
In this paper, we consider the uniform estimate for the oscillatory integral with stationary phase, which was previously studied by Alazard-Burq-Zuily. We significantly reduce the order of required regularity condition on the phase and amplitude functions for the uniform estimate. We also study estimates for the oscillatory integrals of which phase and amplitude functions depend on the oscillation parameter. The novelty of this article lies in the use of the wave packet decomposition, which transforms the decay estimate for the oscillatory integral to the disjointness property of the supports of wave packets. The latter is geometric in its nature and less sensitive to the smoothness of the phase and amplitude functions.
