On the Blaschke-Petkantschin Formula and Drury's Identity

Abstract

The Blaschke-Petkantschin formula is a variant of the polar decomposition of the $k$-fold Lebesgue measure on ${\mathbb{R}}^n$ in terms of the corresponding measures on $k$-dimensional linear subspaces of ${\mathbb{R}}^n$. 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.

10 pages

References in corpus (1)

• A sharp $k$-plane Strichartz inequality for the Schrödinger equation

Cited by in corpus (1)

• Derivation of a Formula of Blaschke and Petkantschin using Probabilistic Ideas