Radon transform on H-type and siegel-type nilpotent groups

Abstract

Let N = V ⊕ Z be a step-two nilpotent group. We study the Radon transform on functions on N defined by integration over the orbits {(2, t)(v, 0); v ∈ V} of the points (z, t) by the action of the subspace V⊕0 of N. For N being of H-type, Siegel-type defined as the Shilov boundary of a complex Siegel domain, or Type F2r,b, a real analogue of the Siegel type, we find an inversion and a Plancherel formula for the Radon transform. We prove certain Lp -Pq boundedness properties for the transform. This generalizes earlier works of Geller-Stein and Strichartz for the Heisenberg groups. © World Scientific Publishing Company.