Abstract
The Lp (where 1≤p≤∞) centroid bodies with respect to weights that are powers of the distance to the origin (i.e., |x|ℓ with ℓ>−n) and their associated isoperimetric inequality (i.e., the polar Lp Busemann-Petty centroid inequality) are introduced in this paper. By means of Ball's body, a corresponding functional version of the polar Lp Busemann-Petty centroid inequality will be also studied.
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