# Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases

## TL;DR

This paper establishes sharp $L^p$ bounds for oscillatory integral operators with homogeneous polynomial phases satisfying a rank one condition, advancing understanding of endpoint estimates in harmonic analysis.

## Contribution

It provides new sharp bounds for a class of oscillatory integrals with polynomial phases under specific rank conditions, including endpoint estimates.

## Key findings

- Sharp $L^p$ bounds for polynomial phase oscillatory integrals
- Endpoint $L^p$ estimates established under rank one condition
- Damping estimates with critical exponents derived

## Abstract

We obtain sharp $L^p$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition which is an important notion introduced by Greenleaf, Pramanik and Tang. Under certain additional assumptions, we can establish sharp damping estimates with critical exponents to prove endpoint $L^p$ estimates.