Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds

Let G(p,n) and G(q,n) be the affine Grassmann manifolds of p- and q-planes in R-n, respectively, and let R-(p,R-q) be the Radon transform from smooth functions on G(p,n) to smooth functions on G(q,n) arising from the inclusion incidence relation. When p < q and dim G(p,n) = dimG(p,n), we present a range characterization theorem for R-(p,R-q) via moment conditions. We then use this range result to prove a support theorem for R-(p,R-q). This complements a previous range characterization theorem for R-(p,R-q) via differential equations when dim G(p, n) < dim G(p, n). We also present a support theorem in this latter case. (c) 2005 Elsevier Inc. All rights reserved.