Let $\tilde{M}$ be the universal cover of a compact pinched\ negatively curved manifold $M$ and $\Gamma=\pi_{1}(M)$ its fundamental group and $\partial \Gamma =\partial \tilde{M}$ its Gromov boundary. Francois Ledrappier claims a bijective correspondence between Hoelder cocycles $c: \Gamma \times \partial \Gamma \to \mathbb{R}$ and zero pressure Hoelder continuous functions $F:T^{1}M\to \mathbb{R}$ on the unit tangent bundle. (Page 105 of Structure au bord des variétés à courbure négative, Séminaire de théorie spectrale et géométrie, Grenoble 1994–1995, (1995), 97–122.)
However, in the above reference Ledrappier seems to not explicitly show that the potential associated to a Hoelder cocycle is Hoelder, but rather leaves it as "obvious". Does any know of an explicit proof of this fact?
