Composition operators on mu-Bloch spaces

Given a positive continuous function mu on the interval 0 < t <= 1, we consider the space of so-called mu-Bloch functions on the unit ball. If mu(t) = t, these are the classical Bloch functions. For mu, we define a metric F(z)(mu)(u) in terms of which we give a characterization of mu-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.