Resumen: 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. Idioma: Inglés DOI: 10.1093/imrn/rnz010 Año: 2021 Publicado en: INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2021, 10 (2021), 7224–7261 ISSN: 1073-7928 Factor impacto JCR: 1.53 (2021) Categ. JCR: MATHEMATICS rank: 67 / 333 = 0.201 (2021) - Q1 - T1 Factor impacto CITESCORE: 2.1 - Mathematics (Q2)