BiBloch mappings and composition operators from Bloch type spaces to BMOA

The problem of constructing functions f 1 , f 2 analytic in the unit disc D of the complex plane satisfying | f 1 ′ ( z ) | + | f 2 ′ ( z ) | ≍ ψ ( 1 1 − | z | ) , z ∈ D , is solved for a wide class of weights ψ that includes normal weights. Several applications are given. Particularly we can generalize known characterizations on Bloch-BMO pullbacks.