  In this paper we study a class of functions that appear naturally in some
equidistribution problems and that we call $F$-harmonic. These are functions of
the universal cover of a closed and negatively curved which possess an integral
representation analogous to the Poisson representation of harmonic functions,
where the role of the Poisson kernel is played by a H\"older continuous kernel.
More precisely we prove a theorem \`a la Fatou about the nontangential
convergence of quotients of such functions, from which we deduce some basic
properties such as the uniqueness of the $F$-harmonic function on a compact
manifold and of the integral representation of $F$-harmonic functions.
