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Rogers-Shephard inequality for log-concave functions


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Author: Alonso Gutiérrez, David
González Merino, Bernardo
JIménez Gömez, Carlos Hugo
Villa Caro, Rafael
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2016-12-01
Published in: Journal of Functional Analysis, 271 (11), 3269-3299.
Document type: Article
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 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.
Cite: 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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DOI: 10.1016/j.jfa.2016.09.005

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