Sobolev embeddings in metric measure spaces with variable dimension

被引：0

作者：

Petteri Harjulehto

Peter Hästö

Visa Latvala

机构：

[1] University of Helsinki,Department of Mathematics and Statistics

[2] University of Oulu,Department of Mathematical Sciences

[3] University of Joensuu,Department of Mathematics

来源：

Mathematische Zeitschrift | 2006年 / 254卷

关键词：

Variable exponent; variable dimension; Hausdorff measure; Lebesgue space; Riesz potential; Hajłasz space; metric measure space; Primary: 46E35; Secondary: 28A78; 28A80; 42B20; 46E30;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this article we study metric measure spaces with variable dimension. We consider Lebesgue spaces on these sets, and embeddings of the Riesz potential in these spaces. We also investigate Hajłasz-type Sobolev spaces, and prove Sobolev and Trudinger inequalities with optimal exponents. All of these questions lead naturally to function spaces with variable exponents.

引用

页码：591 / 609

页数：18

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