$L^2$ estimates of trilinear oscillatory integrals of convolution type on ${\mathbb{R}}^2$

Abstract

This paper is devoted to $L^2$ estimates for trilinear oscillatory integrals of convolution type on ${\mathbb{R}}^2$. The phases in the oscillatory factors include smooth functions and polynomials. We shall establish sharp $L^2$ decay estimates of trilinear oscillatory integrals with smooth phases, and then give $L^2$ uniform estimates for these integrals with polynomial phases.

26 pages