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 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research 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。

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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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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