We provide several factorization theorems for different subspaces of the space of all analytic
functions in the unit disk, in particular we prove a strong factorization theorem for Classical
Hardy classes with Muckenhoupt weights. Proofs are based on a new weighted version of
Coifman-Meyer-Stein theorem on factorization of tent spaces and on properties of an extremal outher function,which was constructed by E. Dynkin.
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