Maximal directional derivatives in Laakso space

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-15 DOI:10.1142/s0219199724500172

Marco Capolli, Andrea Pinamonti, Gareth Speight

引用次数: 0

Abstract

We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a $σ$ -porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a $σ$ -porous set of points. This behavior is completely different to the previously studied settings of Euclidean spaces, Carnot groups and Banach spaces. Hence, the techniques used in these spaces do not generalize to metric measure spaces.

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拉克索空间的最大方向导数

我们研究了定义在拉克索空间上的 Lipschitz 函数的最大方向导数与可微性之间的联系。我们证明，Lipschitz 函数的最大方向导数只意味着σ多孔点集的可微性。另一方面，除了 σ 多孔点集之外，到定点的距离在任何地方都是可微分的。这种行为与之前研究的欧几里得空间、卡诺群和巴拿赫空间完全不同。因此，在这些空间中使用的技术不能推广到公度量空间。

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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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.