Inégalités de Sobolev fractionnaires
We obtain new oscillation inequalities in metric spaces in terms of the PeetreK-functional and the isoperimetric profile. Applications provided include a detailed study of Fractional Sobolev inequalities and the Morrey-Sobolev embedding theorems in different contexts. In particular we include a detai...
| Autores: | , |
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| Tipo de recurso: | libro |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:266919 |
| Acceso en línea: | https://ddd.uab.cat/record/266919 https://dx.doi.org/urn:doi:10.24033/ast.937 |
| Access Level: | acceso abierto |
| Palabra clave: | Sobolev inequalities Modulus of continuity Symmetrization Isoperimetric inequalities Interpolation |
| Sumario: | We obtain new oscillation inequalities in metric spaces in terms of the PeetreK-functional and the isoperimetric profile. Applications provided include a detailed study of Fractional Sobolev inequalities and the Morrey-Sobolev embedding theorems in different contexts. In particular we include a detailed study of Gaussian measures as well as probability measures between Gaussian and exponential. We show a kind of reverse Pólya-Szegö principle that allows us to obtain continuity as a self improvement from boundedness, using symmetrization inequalities. Our methods also allow for precise estimates of growth envelopes of generalized Sobolev and Besov spaces on metric spaces. We also consider embeddings into BMO and their connection to Sobolev embeddings. |
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