  Motivated by applications in fluid dynamics involving the harmonic Bergman
projection we aim at extending the theory of single and double layer potentials
(well documented for functions with $H^1_{\ell oc}$ regularity) to locally
square integrable functions. Having in mind numerical simulations in which
functions are usually defined on a polygonal mesh, we wish this theory to cover
the cases of non-smooth domains (i.e.with Lipschitz continuous or polygonal
boundaries).
