Some sharp null-form type estimates for the Klein--Gordon equation

TL;DR

This paper proves a sharp bilinear estimate for the Klein-Gordon propagator, leading to new null-form and Strichartz estimates, advancing the understanding of dispersive PDEs.

Contribution

It introduces a novel sharp bilinear estimate for the Klein-Gordon equation, inspired by wave equation techniques, and derives related sharp null-form and Strichartz estimates.

Findings

Established a sharp bilinear estimate for Klein-Gordon propagator

Derived several sharp null-form type estimates

Recovered existing sharp Strichartz estimates

Abstract

We establish a sharp bilinear estimate for the Klein--Gordon propagator in the spirit of recent work of Beltran--Vega. Our approach is inspired by work in the setting of the wave equation due to Bez, Jeavons and Ozawa. As a consequence of our main bilinear estimate, we deduce several sharp estimates of null-form type and recover some sharp Strichartz estimates found by Quilodr\'an and Jeavons.