Calculus of Variations and Geometric Measure Theory

H. Bahouri - D. Barilari - I. Gallagher

Strichartz estimates and Fourier restriction theorems on the Heisenberg group

created by barilari on 09 Nov 2019
modified on 15 Mar 2021


Published Paper

Inserted: 9 nov 2019
Last Updated: 15 mar 2021

Journal: Journal of Fourier Analysis and Applications
Volume: 27
Number: 21
Year: 2021
Doi: 10.1007/s00041-021-09822-5
Links: Link to ArXiv


This paper is dedicated to the proof of Strichartz estimates on the Heisenberg group $\mathbb{H}^d$ for the linear Schrödinger and wave equations involving the sublaplacian. The Schrödinger equation on $\mathbb{H}^d$ 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 by Tomas and Stein, is based on Fourier restriction theorems on $\mathbb{H}^d$, 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.