In this paper, we prove that the Kato smoothing effects for magnetic half wave operators can yield the endpoint Strichartz estimates for linear wave equations with magnetic potentials on the two dimensional hyperbolic spaces. As a corollary, we obtain the endpoint Strichartz estimates in the case of small potentials. This result serves as a cornerstone for the author's work [27] and collaborative work [29] in the study of asymptotic stability of harmonic maps for wave maps from $ \mathbb R\times \mathbb H^2$ to $ \mathbb H^2$.

中文翻译：

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端点Strichartz估计二维双曲空间上的电磁波方程

在本文中，我们证明了磁半波算子的Kato平滑效应可以产生二维双曲空间上具有磁势的线性波动方程的端点Strichartz估计。作为推论，在小电位的情况下，我们获得了终点Strichartz估计。该结果为作者的工作[27]和协作工作[29]（从$ \ mathbb R \ times \ mathbb H ^ 2 $到$ \ mathbb H ^）波动图的谐波图的渐近稳定性研究提供了基础。 2 $。