On Rogers-Shephard type inequalities for general measures

TL;DR

This paper extends Rogers-Shephard inequalities to convex bodies under measures with specific density properties, providing new functional inequalities and broadening classical geometric results.

Contribution

It introduces Rogers-Shephard type inequalities for convex bodies with radially decreasing or quasi-concave measures, including functional versions of classical inequalities.

Findings

Established Rogers-Shephard inequalities for measures with radially decreasing densities.

Derived functional versions of classical Rogers-Shephard inequalities.

Extended geometric inequalities to broader measure classes.

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.