Orlicz John ellipsoids

摘要

The Orlicz-John ellipsoids, which are in the framework of the booming Orlicz Brunn-Minkowski theory, are introduced for the first time. It turns out that they are generalizations of the classical John ellipsoid and the evolved L-p John ellipsoids. The analog of Ball's volume-ratio inequality is established for the new Orlicz-John ellipsoids. The connection between the isotropy of measures and the characterization of Orlicz-John ellipsoids is demonstrated. (C) 2014 Elsevier Inc. All rights reserved.