Klein-Gordon方程的一些明显的零形式估计

Pub Date : 2021-02-05 DOI:10.2969/jmsj/86418641

Jayson Cunanan, Shobu Shiraki

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摘要

根据Beltran–Vega最近的工作精神，我们建立了Klein–Gordon传播算子的一个尖锐双线性估计。我们的方法受到了Bez、Jeavons和Ozawa在波动方程设置方面的工作的启发。作为我们的主要双线性估计的结果，我们推导了几种零形式类型的尖锐估计，并恢复了Quilodrán和Jeavons发现的一些尖锐的Strichartz估计。

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

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 Quilodrán and Jeavons.

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