Trigonometric chaos and Xp inequalities, I : Balanced Fourier truncations over discrete groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-21 DOI:10.2140/apde.2024.17.2561

Antonio Ismael Cano-Mármol, José M. Conde-Alonso, Javier Parcet

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引用次数: 0

Abstract

We investigate $L_{p}$ -estimates for balanced averages of Fourier truncations in group algebras, in terms of “differential operators” acting on them. Our results extend a fundamental inequality of Naor for the hypercube (with profound consequences in metric geometry) to discrete groups. Different inequalities are established in terms of “directional derivatives” which are constructed via affine representations determined by the Fourier truncations. Our proofs rely on the Banach $X_{p}$ nature of noncommutative $L_{p}$ -spaces and dimension-free estimates for noncommutative Riesz transforms. In the particular case of free groups we use an alternative approach based on free Hilbert transforms.

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三角混沌和 Xp 不等式，I：离散群上的平衡傅立叶截断

我们从作用于群集的 "微分算子 "的角度，研究了群集中傅里叶截断的平衡平均数的 Lp 估计值。我们的结果将纳奥尔的超立方体基本不等式（对度量几何有深远影响）扩展到了离散群。不同的不等式是通过 "方向导数 "建立的，而 "方向导数 "是通过由傅里叶截断决定的仿射表示来构建的。我们的证明依赖于非交换 Lp 空间的 Banach X p 性质和非交换里兹变换的无维度估计。在自由群组的特殊情况下，我们使用了基于自由希尔伯特变换的另一种方法。

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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.