Composition operators between Bloch-type spaces in the polydisc

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We characterize those holomorphic mappings ψ from the polydisc Dn in Cn to itself for which the induced composition operators Cψ are bounded (or compact) from the Bloch-type space Bω to βμ (respectively, from the little Bloch-type space Bω,0 to Bμ,0),where ω is a normal function on [0, 1) andμ is a nonnegative function on [0, 1) withμ(tn) > 0for some sequence {tn}n∞n=1(∪) [0, 1) satisfying limn→∞ tn = 1.
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