In Metric-measure Spaces Sobolev Embedding is Equivalent to a Lower Bound for the Measure

被引：13

作者：

Gorka, Przemysaw ^{[1
]}

机构：

[1] Warsaw Univ Technol, Dept Math, Informat Sci, Ul Koszykowa 75, PL-00662 Warsaw, Poland

来源：

POTENTIAL ANALYSIS | 2017年 / 47卷 / 01期

关键词：

Sobolev spaces; Sobolev inequalities; Metric measure spaces; Lower bound for measure;

D O I：

10.1007/s11118-016-9605-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Sobolev inequalities on doubling metric measure spaces. We investigate the relation between Sobolev embeddings and lower bound for measure. In particular, we prove that if the Sobolev inequality holds, then the measure mu satisfies the lower bound, i.e. there exists b such that mu(B(x,r))ae<yen>b r (alpha) for ra(0,1] and any point x from metric space.

引用

页码：13 / 19

页数：7

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