On bm$(p,q)$-John ellipsoids

Abstract

In this paper, the (p, q)-John ellipsoids are introduced and characterized. The classical John ellipsoid and the Lp John ellipsoids are special cases of the (p, q)-John ellipsoids. The continuity of the (p, q)-John ellipsoids is investigated. Analogues of Ball's volume-ratio inequality and John's inclusion for the (p, q)-John ellipsoids are established.