Lp$L_p$‐cosine transform of the (p,q)${(p,q)}$‐th dual curvature measure

Abstract

AbstractThe ‐th dual curvature measure was introduced by Lutwak, Yang and Zhang. In this paper, we study the cosine transform of the ‐th dual curvature measure which defines a new convex body. We prove that the new convex body unifies the Petty projection body and the centroid body. The corresponding affine isoperimetric inequality is also obtained. It is an extension of the known Petty projection inequality.