A note on the Blaschke-Petkantschin formula, Riesz distributions, and drury's identity

Document Type

Article

Publication Date

12-19-2018

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 famous formula and discuss its connection with Riesz distributions associated with fractional powers of the Cayley-Laplace operator on matrix spaces. Another application of our proof is the celebrated Drury identity that plays a key role in the study of mapping properties of the Radon-John k-plane transforms. Our proof gives precise meaning to the constants in Drury's identity and to the class of admissible functions.

Publication Source (Journal or Book title)

Fractional Calculus and Applied Analysis

First Page

1641

Last Page

1650

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