Capacities and Density Conditions in Metric Spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-30 DOI:10.1007/s11118-024-10137-5

Javier Canto, Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas

引用次数: 0

Abstract

We examine the relations between different capacities in the setting of a metric measure space. First, we prove a comparability result for the Riesz \((\beta ,p)\)-capacity and the relative Hajłasz \((\beta ,p)\)-capacity, for \(1<p<\infty \) and \(0<\beta \le 1\), under a suitable kernel estimate related to the Riesz potential. Then we show that in geodesic spaces the corresponding capacity density conditions are equivalent even without assuming the kernel estimate. In the last part of the paper, we compare the relative Hajłasz (1, p)-capacity to the relative variational p-capacity.

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公制空间中的容量和密度条件

我们研究了在度量空间中不同容量之间的关系。首先，我们证明了在（1<p<infty \）和（0<beta \le 1\）下，在与Riesz势相关的合适的核估计下，Riesz \（（beta ,p））-容量和相对Hajłasz \（（beta ,p））-容量的可比性结果。然后我们证明，在测地空间中，即使不假设核估计，相应的容量密度条件也是等价的。在本文的最后一部分，我们将相对 Hajłasz (1, p) 容量与相对变分 p 容量进行比较。

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.