Sobolev embeddings in metric measure spaces with variable dimension

Petteri Harjulehto, Peter Hästö, Visa Latvala

Research output: Contribution to journalArticleScientificpeer-review


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 languageEnglish
JournalMathematische Zeitschrift
Issue number3
Pages (from-to)591-609
Number of pages19
Publication statusPublished - 2006
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

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