This paper is dedicated to the proof of Strichartz estimates on the Heisenberg group \({\mathop {\mathbb H}\nolimits }^d\) for the linear Schrödinger and wave equations involving the sublaplacian. The Schrödinger equation on \({\mathop {\mathbb H}\nolimits }^d\) is an example of a totally non-dispersive evolution equation: for this reason the classical approach that permits to obtain Strichartz estimates from dispersive estimates is not available. Our approach, inspired by the Fourier transform restriction method initiated in Tomas (Bull Am Math Soc 81: 477–478, 1975), is based on Fourier restriction theorems on \({\mathop {\mathbb H}\nolimits }^d\), using the non-commutative Fourier transform on the Heisenberg group. It enables us to obtain also an anisotropic Strichartz estimate for the wave equation, for a larger range of indices than was previously known.

本文致力于证明Heisenberg群 \（{\ mathop {\ mathbb H} \ nolimits} ^ d \）上关于次拉普拉斯方程的线性Schrödinger和波动方程的Strichartz估计。\（{\ mathop {\ mathbb H} \ nolimits} ^ d \）上的Schrödinger方程是一个完全非分散的演化方程的示例：由于这个原因，允许从分散的估计中获得Strichartz估计的经典方法不是可用的。我们的方法是受Tomas中发起的傅立叶变换限制方法启发的（Bull Am Math Soc 81：477–478，1975），基于 \（{\ mathop {\ mathbb H} \ nolimits} ^ d \ ），在Heisenberg组上使用非交换傅立叶变换。它使我们还能获得波动方程的各向异性Strichartz估计，其指数范围比以前已知的更大。