The well-known stationary phase formula gives us a way to precisely compute 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.
Asymptotic estimates of oscillatory integrals with general phase and singular amplitude: Applications to dispersive equations
The Wave Equation on Lattices and Oscillatory Integrals
Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals
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