  We present a nonvariational setting for the Neumann problem for harmonic
functions that are H\"{o}lder continuous and that may have infinite Dirichlet
integral. Then we introduce a space of distributions on the boundary (a space
of first order traces for H\"{o}lder continuous harmonic functions), we analyze
the properties of the corresponding distributional single layer potential and
we prove a representation theorem for harmonic H\"{o}lder continuous functions
in terms of distributional single layer potentials. As an application, we solve
the interior and exterior Neumann problem with distributional data in the space
of first order traces that has been introduced.
