  We obtain new descriptions of the null spaces of several projectively
equivalent transforms in integral geometry. The paper deals with the hyperplane
Radon transform, the totally geodesic transforms on the sphere and the
hyperbolic space, the spherical slice transform, and the Cormack-Quinto
spherical mean transform for spheres through the origin. The consideration
extends to the corresponding dual transforms and the relevant exterior/interior
modifications. The method relies on new results for the Gegenbauer-Chebyshev
integrals, which generalize Abel type fractional integrals on the positive
half-line.
