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...

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Detalhes bibliográficos
Autores: Haddad, Julián Eduardo, Jiménez Gómez, Carlos Hugo, Da Silva Montenegro, Marcos
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
Descrição
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.