中文摘要：

该文研究了四元数海森堡群上与full-Laplacian算子相关的波方程的解的估计.通过研究四元数海森堡群上的full-Laplacian算子,得到了该算子的一些重要性质和四元数海森堡群上的Littlewood-Paley理论.讨论了四元数海森堡群上一些重要的函数空间的性质.得到了波方程的解的色散估计和Strichartz估计.

英文摘要：

In this article, we prove dispersive and Strichartz estimates for the solution of the wave equation related to the full-Laplacian on the quaternion Heisenberg group, by means of homogeneous Besov space defined by a Littlewood-Paley decomposition related to the full- Laplacian.