Sobolev embeddings in metric measure spaces with variable dimension

Petteri Harjulehto; Peter Hästö; Visa Latvala

doi:10.1007/s00209-006-0960-8

Sobolev embeddings in metric measure spaces with variable dimension

Petteri Harjulehto, Peter Hästö, Visa Latvala

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

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 Hajlasz-type Sobolev spaces, and prove Sobolev and Trudinger inequalities with optimal exponents. All of these questions lead naturally to function spaces with variable exponents.

Original language	English
Journal	Mathematische Zeitschrift
Volume	254
Issue number	3
Pages (from-to)	591-609
Number of pages	19
ISSN	0025-5874
DOIs	https://doi.org/10.1007/s00209-006-0960-8
Publication status	Published - 2006
MoE publication type	A1 Journal article-refereed

Fields of Science

111 Mathematics

Access to Document

10.1007/s00209-006-0960-8

Cite this

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AB - 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 Hajlasz-type Sobolev spaces, and prove Sobolev and Trudinger inequalities with optimal exponents. All of these questions lead naturally to function spaces with variable exponents.

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