Abstract
Let Un be the unit polydisc of ℂn and
φ=(φ1,…,φn) a holomorphic self-map of Un. ℬp(Un), ℬ0p(Un), and B0*p(Un) denote the p-Bloch space, little p-Bloch space,
and little star p-Bloch space in the unit polydisc Un, respectively, where p,q>0. This paper gives the estimates of the
essential norms of bounded composition operators Cφ induced
by φ between ℬp(Un) (ℬ0p(Un)
or B0*p(Un)) and ℬq(Un) (ℬ0q(Un)
or B0*p(Un)). As their applications, some necessary and
sufficient conditions for the (bounded) composition operators
Cφ to be compact from ℬp(Un) (ℬ0p(Un)
or ℬ0∗p(Un)) into ℬq(Un) (ℬ0q(Un)
or B0*p(Un)) are obtained.