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Sobolev embeddings in metric measure spaces with variable dimension |
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| Authors: | Petteri Harjulehto Peter Hästö Visa Latvala |
| Affiliation: | (1) Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014, Finland;(2) Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Finland;(3) Department of Mathematics, University of Joensuu, P.O. Box 111, Fin-80101 Joensuu, Finland |
| 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 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. Supported the Research Council of Norway, Project 160192/V30. |
| Keywords: | Variable exponent variable dimension Hausdorff measure Lebesgue space Riesz potential Hajł asz space metric measure space |
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