Composition operator on F(p,q,s) spaces in the unit ball of Cn

In this paper, the authors characterize those phi, holomorphic self-maps of B, for which the composition operator C-phi is bounded (or compact) on F(p,q,s) in some cases. Moreover, the following results are given. (1)If 1 < p < q + n + 1 and C phi satisfies some boundedness conditions, then C-phi is compact on F(p,q,s) if and only if<br />lim(|z|-> 1-)1-|z|(2 )/1-|phi(z)|2=0. (2) If 1 <= p <infinity and q+n+1 < p <infinity, then C-phi is a compact operator on F(p,q,s) if and only if ?phi?(infinity)< 1 and phi(l)is an element of F(p,q,s) for all l is an element of{1,2, horizontexpressionl ellipsis ,n}.