Article
Rogers-Shephard inequality for log-concave functions
Author/s | Alonso Gutiérrez, David
González Merino, Bernardo JIménez Gömez, Carlos Hugo Villa Caro, Rafael |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2016-12-01 |
Deposit Date | 2016-11-29 |
Published in |
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Abstract | In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and ... In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets. |
Project ID. | MTM2013-42105-P
P1-1B2014-35 info:eu-repo/grantAgreement/MINECO/MTM2012-34037 info:eu-repo/grantAgreement/MINECO/MTM2012-30748 |
Citation | Alonso Gutiérrez, D., González Merino, B., JIménez Gömez, C.H. y Villa Caro, R. (2016). Rogers-Shephard inequality for log-concave functions. Journal of Functional Analysis, 271 (11), 3269-3299. |
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