Sobolev algebra counterexamples

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

Abstract

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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索博列夫代数反例

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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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

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