Riesz potentials and integral geometry in the space of rectangular matrices

Document Type

Article

Publication Date

10-1-2006

Abstract

Riesz potentials on the space of rectangular n × m matrices arise in diverse "higher rank" problems of harmonic analysis, representation theory, and integral geometry. In the rank-one case m = 1 they coincide with the classical operators of Marcel Riesz. We develop new tools and obtain a number of new results for Riesz potentials of functions of matrix argument. The main topics are the Fourier transform technique, representation of Riesz potentials by convolutions with a positive measure supported by submanifolds of matrices of rank< m, the behavior on smooth and Lp functions. The results are applied to investigation of Radon transforms on the space of real rectangular matrices. © 2005 Elsevier Inc. All rights reserved.

Publication Source (Journal or Book title)

Advances in Mathematics

First Page

549

Last Page

598

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