  In the framework of Clifford analysis, a chain of harmonic and monogenic
potentials in the upper half of (m+1)-dimensional Euclidean space was recently
constructed, including a higher dimensional analogue of the logarithmic
function in the complex plane, and their distributional boundary values were
computed. In this paper we determine these potentials in lower half-space, and
investigate whether they can be extended through the boundary R^m. This is a
stepping stone to the representation of a doubly infinite sequence of
distributions in R^m, consisting of positive and negative integer powers of the
Dirac and the Hilbert-Dirac operators, as the jump across R^m of monogenic
functions in the upper and lower half-spaces, in this way providing a sequence
of interesting examples of Clifford hyperfunctions.

Functional Analysis;Classical Analysis and ODEs;Complex Variables