Decay Rate of n-Linear Oscillatory Integral Operators in $\mathbb{R}^2$

TL;DR

This paper establishes sharp $L^p$ decay estimates for multilinear oscillatory integrals in two dimensions, generalizing previous results and providing a deeper understanding of their decay behavior.

Contribution

It extends prior work by Gressman and Xiao to more general multilinear oscillatory integrals in $\

Findings

Proved sharp $L^p$ decay estimates for multilinear oscillatory integrals in $\

Generalized previous results to broader classes of integrals

Established the decay rate using a scaling argument

Abstract

In this paper, we prove $L^p$ decay estimates for multilinear oscillatory integrals in $\mathbb{R}^2$, establishing sharpness through a scaling argument. The result in this paper is a generalization of the previous work by Gressman and Xiao (2016).