Strichartz Estimates and Fourier Restriction Theorems on the Heisenberg Group

被引：3

作者：

Bahouri, Hajer ^{[1
,2
]}

Barilari, Davide ^{[3
]}

Gallagher, Isabelle ^{[4
,5
]}

机构：

[1] CNRS, 4 Pl Jussieu, F-75005 Paris, France

[2] Sorbonne Univ, Lab Jacques Louis Lions LJLL UMR 7598, 4 Pl Jussieu, F-75005 Paris, France

[3] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, Padua, Italy

[4] PSL Res Univ, CNRS, DMA UMR 8553, Ecole Normale Super, F-75005 Paris, France

[5] Univ Paris, UFR Math, F-75005 Paris, France

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2021年 / 27卷 / 02期

关键词：

Partial differential equations on the Heisenberg group; Strichartz estimates;

D O I：

10.1007/s00041-021-09822-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is dedicated to the proof of Strichartz estimates on the Heisenberg group H-d for the linear Schrodinger and wave equations involving the sublaplacian. The Schrodinger 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 in Tomas (Bull Am Math Soc 81: 477-478, 1975), 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.

引用

页数：41

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