  The notion of the Radon transform on the Heisenberg group was introduced by
R. Strichartz and inspired by D. Geller and E.M. Stein's related work. The more
general transversal Radon transform integrates functions on the m-dimensional
real Euclidean space over hyperplanes meeting the last coordinate axis. We
obtain new boundedness results and explicit inversion formulas for both
transforms on $L^p$ functions in the full range of the parameter $p$. We also
show that these transforms are isomorphisms of the corresponding
Semyanistyi-Lizorkin spaces of smooth functions. In the framework of these
spaces we obtain inversion formulas, which are pointwise analogues of the
corresponding formulas by R. Strichartz.
