索博列夫代数反例

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-05-13 DOI:10.4171/JFG/59

T. Coulhon, Luke G. Rogers

引用次数: 0

摘要

在欧几里得条件下，Sobolev空间$W^{\alpha,p}\cap L^\infty$是$\alpha>0$和$p\in(1,\infty)$点积的代数。这个性质最近被扩展到各种几何设置。我们产生了一类分形的例子，其中它在很大范围内的指标$\alpha,p$失败。

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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Sobolev algebra counterexamples

In the Euclidean setting the Sobolev spaces $W^{\alpha,p}\cap L^\infty$ are algebras for the pointwise product when $\alpha>0$ and $p\in(1,\infty)$. This property has recently been extended to a variety of geometric settings. We produce a class of fractal examples where it fails for a wide range of the indices $\alpha,p$.

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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.