Let be the set of all holomorphic functions in the open unit disk . For , the weighted Bloch space is the set of all functions in for which
and is the space of all for which
where is planar Lebesgue measure. Here, as usual, is the Carleson square associated with the arc .
For analytic selfmaps of , the author characterizes those composition operators , , that are bounded, respectively compact. Also, necessary and sufficient conditions on the Taylor coefficients of a lacunary Taylor series are given that imply that .