Integral Transforms of Signumdistributions

Expressing distributions in Euclidean space in terms of spherical coordinates gives rise to an alternative class of continuous linear functionals, termed signumdistributions, acting on test functions showing a pointwise singularity at the origin. In this paper the theory of signumdistributions is further explored from the viewpoint of integral transforms, viz. the Fourier and Hilbert transforms, and the interplay between them.