  In this paper, we study representations for three-point Lie algebras of genus
zero based on the Cox-Jurisich's presentations. We construct two functors which
transform simple restricted modules with nonzero levels over the standard
affine algebras into simple modules over the three-point affine algebras of
genus zero. As a corollary, vertex representations are constructed for the
three-point affine algebra of genus zero using vertex operators. Moreover, we
construct a Fock module for certain quotient of three-point Virasoro algebra of
genus zero.
