Abstract: By using analysis methods and constructing test functions
we obtained some new equivalent conditions for the boundedness and
compactness of the integral-type operator $C_\varphi ^g $ from the
minimal M$\ddot{\rm o}$bius invariant space into the Bloch-type
space. These equivalent conditions give perfect characterizations of
$C_\varphi ^g $, which also provide good reference for the study of
other integral-type operators.

Key words: Mobius invariant space, Bloch-type space, integral-type operator