# Stationary phase type estimates for low symbol regularity

## TL;DR

This paper develops decay bounds for oscillatory integrals with symbols of low regularity, extending stationary phase estimates to less smooth cases relevant in various applications.

## Contribution

It introduces new decay bounds for oscillatory integrals with low regularity symbols, broadening the applicability of stationary phase methods.

## Key findings

- Derived decay bounds for integrals with irregular symbols
- Extended stationary phase estimates to less regular symbols
- Applicable to problems with low regularity conditions

## Abstract

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.