A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury’s identity

Abstract

The Blaschke-Petkantschin formula is a variant of the polar decomposition of the k-fold Lebesgue measure on R n in terms of the corresponding measures on k-dimensional linear subspaces of R n . We suggest a new elementary proof of this formula and discuss its connection with the celebrated Drury's identity that plays a key role in the study of mapping properties of the Radon-John k-plane transforms. We give a new derivation of this identity and provide it with precise information about constant factors and the class of admissible functions.2010 Mathematics Subject Classification. Primary 44A12; Secondary 28A75, 60D05.