000057928 001__ 57928 000057928 005__ 20200221144223.0 000057928 0247_ $$2doi$$a10.1016/j.jfa.2016.09.005 000057928 0248_ $$2sideral$$a96982 000057928 037__ $$aART-2016-96982 000057928 041__ $$aeng 000057928 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso-Gutiérrez, D.$$uUniversidad de Zaragoza 000057928 245__ $$aRogers–Shephard inequality for log-concave functions 000057928 260__ $$c2016 000057928 5060_ $$aAccess copy available to the general public$$fUnrestricted 000057928 5203_ $$aIn 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. 000057928 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2013-42105-P 000057928 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000057928 590__ $$a1.254$$b2016 000057928 591__ $$aMATHEMATICS$$b37 / 310 = 0.119$$c2016$$dQ1$$eT1 000057928 592__ $$a2.46$$b2016 000057928 593__ $$aAnalysis$$c2016$$dQ1 000057928 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000057928 700__ $$aGonzález Merino, B. 000057928 700__ $$aJiménez, C.H. 000057928 700__ $$aVilla, R. 000057928 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000057928 773__ $$g271, 11 (2016), 3269-3299$$pJ. funct. anal.$$tJOURNAL OF FUNCTIONAL ANALYSIS$$x0022-1236 000057928 8564_ $$s520928$$uhttps://zaguan.unizar.es/record/57928/files/texto_completo.pdf$$yPreprint 000057928 8564_ $$s41775$$uhttps://zaguan.unizar.es/record/57928/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000057928 909CO $$ooai:zaguan.unizar.es:57928$$particulos$$pdriver 000057928 951__ $$a2020-02-21-13:16:22 000057928 980__ $$aARTICLE