On Rogers-Shephard type inequalities for general measures

Abstract

In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the origin. Functional versions of classical Rogers-Shephard inequalities are also derived as consequences of our approach.

Added references. Revised discussion in section 2, with new Theorem 2.2. Corrected typos. Main results unchanged