I attributed the proof that the isometry groups of a Gromov hyperbolic space acts as a convergence group on its boundary to Bowditch (1996). This is more commonly attributed to Tukia (1994). Furthermore, Woess did publish the same result one year prior (1993). The same paper by Woess discusses the Dirichlet problem in a similar context, so it should also have been cited in Section 4.2.