Maximal Decay Inequalities for Trilinear oscillatory integrals of convolution type

Abstract

In this paper we prove sharp $L^{\infty }$-$L^{\infty }$-$L^{\infty }$ decay for certain trilinear oscillatory integral forms of convolution type on ${\mathbb{R}}^2$. These estimates imply earlier $L^2$-$L^2$-$L^2$ results obtained by the second author as well as corresponding sharp, stable sublevel set estimates of the form studied by Christ and Christ, Li, Tao, and Thiele. New connections to the multilinear results of Phong, Stein, and Sturm are also considered.

References in corpus (2)

• Multilinear Oscillatory Integrals Via Reduction of Dimension
• Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities

Cited by in corpus (1)

• Endpoint estimates for one-dimensional oscillatory integral operator