关于$F$ -调和函数的Fatou定理
A Fatou theorem for $F$-harmonic functions
摘要：
本文研究了一类自然出现在等分布问题中的函数，我们称之为$F$ -调和函数。这些都是函数的通用覆盖的封闭和负弯曲，拥有整表示类似的泊松表示的调和函数，其中的作用，泊松核是发挥霍德尔连续内核。更确切地说，我们证明了一个定理à la Fatou关于非切收敛的这类功能，从我们推出的一些基本性质，如唯一性的$F$ -调和函数在一个紧凑的流形和整表示的$F$ -调和函数。
英文摘要：
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 Hölder continuous kernel. More precisely we prove a theorem à 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.
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