On compact composition operators on a class of holomorphic function spaces over the unit ball in ℂn

In this paper, a general function space X(Bn) over the unit ball in ℂn with norm ∥ · ∥X(Bn) is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X(Bn), related to works of [8] and [10].