Rogers–Shephard inequality for log-concave functions

Alonso-Gutiérrez, D. (Universidad de Zaragoza) ; González Merino, B. ; Jiménez, C.H. ; Villa, R.

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jfa.2016.09.005

Año: 2016

Publicado en: JOURNAL OF FUNCTIONAL ANALYSIS 271, 11 (2016), 3269-3299
ISSN: 0022-1236

Factor impacto JCR: 1.254 (2016)

Categ. JCR: MATHEMATICS rank: 37 / 310 = 0.119 (2016) - Q1 - T1

Factor impacto SCIMAGO: 2.46 - Analysis (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2013-42105-P

Tipo y forma: Article (PrePrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)