Strichartz estimates and Fourier restriction theorems on the Heisenberg group

Abstract : This paper is dedicated to the proof of Strichartz estimates on the Heisen-berg group H^d for the linear Schrödinger and wave equations involving the sublaplacian. The Schrödinger equation on 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 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [43 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02357244
Contributor : Davide Barilari <>
Submitted on : Saturday, November 9, 2019 - 5:19:27 PM
Last modification on : Thursday, November 14, 2019 - 1:38:27 AM

File

StricHeis_8nov.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02357244, version 1

Citation

Hajer Bahouri, Davide Barilari, Isabelle Gallagher. Strichartz estimates and Fourier restriction theorems on the Heisenberg group. 2019. ⟨hal-02357244⟩

Share

Metrics

Record views

17

Files downloads

15