The well-known stationary phase formula gives us a way to find asymptotics of oscillating integrals so long as the symbol is regular enough (in comparison to the large parameter controlling the oscillation). However in a number of applications we find ourselves with symbols that are not suitably regular. In this paper we obtain decay bounds for such oscillatory integrals.

中文翻译：

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低符号规律性的稳态相位类型估计

只要符号足够规则（与控制振荡的大参数相比），众所周知的固定相公式为我们提供了一种找到振荡积分的渐近线的方法。然而，在许多应用程序中，我们发现自己使用的符号并不合适。在本文中，我们获得了这种振荡积分的衰减界限。