A bilinear approach to cone multipliers II. Applications

Abstract.

This paper is a continuation of [TV], in which new bilinear estimates for surfaces in ${\bold R}^3$ were proven. We give a concrete improvement to the square function estimate of Mockenhaupt [M]. We apply these estimates to give new progress on several open problems concerning the wave and Schrödinger equation in ${\bold R}^2+1$, and convolution with curves in ${\bold R}^3$.