海森堡类型群上具有 p 特定锐正则约束的 $$L^p$$ 谱乘数定理

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Fourier Analysis and Applications Pub Date : 2024-04-04 DOI:10.1007/s00041-024-10075-1

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引用次数: 0

摘要

摘要我们证明了海森堡类型群上的子拉普拉斯在尖锐正则条件 $s>d\left| 1/p-1/2\right| $ 下的$L^p$ -谱乘数定理，其中 d 是底层群的拓扑维数。我们的方法依赖于限制型估计，在限制型估计中，乘数会沿着拉普拉奇在群中心的谱被截断。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An $$L^p$$ -Spectral Multiplier Theorem with Sharp p-Specific Regularity Bound on Heisenberg Type Groups

Abstract

We prove an $L^p$ -spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition $s>d\left| 1/p-1/2\right| $ , where d is the topological dimension of the underlying group. Our approach relies on restriction type estimates where the multiplier is additionally truncated along the spectrum of the Laplacian on the center of the group.

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来源期刊

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications