Abstract
Let be the unit polydisc of
and
a holomorphic self-map of
.
,
and
denote the
-Bloch space, little
-Bloch space, and little star
-Bloch space in the unit polydisc
, respectively, where
. This paper gives the estimates of the essential norms of bounded composition operators
induced by
between
(
or
) and
(
or
). As their applications, some necessary and sufficient conditions for the (bounded) composition operators
to be compact from
(
or
) into
(
or
) are obtained.