It is shown that the Hankel transformation H_v acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of H_v which holds on L²  is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line   as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation. The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1+1 dimensional edge-degenerate wave equation is given.