Strichartz estimates and Fourier restriction theorems on the Heisenberg group

2019/11/09 by Bahouri, Hajer, Barilari, Davide, Gallagher, Isabelle · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1911.03729

Abstract

This paper is dedicated to the proof of Strichartz estimates on the Heisenberg 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.

Cited by

• Decay estimates for a class of dispersive equations with partial inverse-square potentials
• Strichartz estimates and its application to the well-posedness of the nonlinear Schrödinger equations on H-type groups
• Dispersive equations with invariant measures
• Local Dispersive and Strichartz estimates for the Schrödinger equation associated to the Ornstein-Uhlenbeck operator

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