论文标题
海森堡组的一类波动方程的衰减估计值
Decay estimates for a class of wave equations on the Heisenberg group
论文作者
论文摘要
在本文中，我们研究了Heisenberg Group $ h^n $的一类分散波方程。基于$ h^n $的组傅立叶变换，laguerre函数的属性和固定阶段的引理，我们建立了$ e^{itx（\ natcal {l}）} $ h^n $一类分散半群的衰减估计值， $ \ Mathcal {l} $是$ h^n $上的sub-laplacian。最后，使用二元参数，我们将获得的结果应用于某些特定方程的解，例如分数Schrödinger方程，分数波方程和第四阶Schrödinger方程。
In this paper, we study a class of dispersive wave equations on the Heisenberg group $H^n$. Based on the group Fourier transform on $H^n$, the properties of the Laguerre functions and the stationary phase lemma, we establish the decay estimates for a class of dispersive semigroup on $H^n$ given by $e^{itϕ(\mathcal{L})}$, where $ϕ: \mathbb{R}^+ \to \mathbb{R}$ is smooth, and $\mathcal{L}$ is the sub-Laplacian on $H^n$. Finally, using the duality arguments, we apply the obtained results to derive the Strichartz inequalities for the solutions of some specific equations, such as the fractional Schrödinger equation, the fractional wave equation and the fourth-order Schrödinger equation.
