度量空间中的Hardy-Sobolev不等式和加权容量

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2021-06-10 DOI:10.7146/math.scand.a-133257

L. Ihnatsyeva, Juha Lehrback, Antti V. Vahakangas

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引用次数: 0

摘要

设$\Omega$是度量空间$X$中的开集。我们的主要结果给出了$\Omega$中加权Hardy–Sobolev不等式的有效性和关于$\Omega$的Whitney覆盖的加权容量的拟可加性之间的等价性。证明中的重要成分包括使用离散卷积作为容量测试函数，以及加权Hardy–Sobolev不等式的Maz'ya型表征。

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Hardy-Sobolev inequalities and weighted capacities in metric spaces

Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy–Sobolev inequality in $\Omega$ and quasiadditivity of a weighted capacity with respect to Whitney covers of $\Omega$. Important ingredients in the proof include the use of a discrete convolution as a capacity test function and a Maz'ya type characterization of weighted Hardy–Sobolev inequalities.

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.