A sharp Rogers-Shephard type inequality for Orlicz-difference body of planar convex bodies (Q2018811)

The authors discuss natural extensions of classical convexity notions to Orlicz spaces. More precisely, they prove a sharp Orlicz type analogue of the classical Rogers-Shephard inequality on the volume of the difference body, using also the notion of shadow systems of families of convex bodies. Thus, with this work, results of \textit{C. Bianchini} and \textit{A. Colesanti} [Proc. Am. Math. Soc. 136, No. 7, 2575--2582 (2008; Zbl 1143.52008)] are extended.