Sharp affine Sobolev type inequalities via the Lp Busemann–Petty centroid inequality
We show that the Lp Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg inequalities. Our approach allows also to characterize directly the co...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/46761 |
| Acesso em linha: | http://hdl.handle.net/11441/46761 https://doi.org/10.1016/j.jfa.2016.03.017 |
| Access Level: | acceso abierto |
| Palavra-chave: | Lp Busemann-Petty centroid inequality Affine logarithmic inequalities Affine Sobolev inequalities |
| Resumo: | We show that the Lp Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg inequalities. Our approach allows also to characterize directly the corresponding equality cases. |
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