VOLUME INEQUALITIES FOR L_p-JOHN ELLIPSOIDS AND THEIR DUALS

Abstract

Abstract. In this paper, we establish some inequalities among the L p -centroid body, the L p -polar projection body, the L p -John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the L p -centroid body, the L p -polar projection body, the L p -John ellipsoid and its dual.2000 Mathematics Subject Classification. 52A40, 52A20. In this paper, we continue the study of the volume inequalities among the L pcentroid body the L p -polar projection body, the L p -John ellipsoid and its dual.The setting for this paper is n-dimensional Euclidean space ‫ޒ‬ n . Let K n denote the set of convex bodies (compact, convex subsets with non-empty interiors). Let K