Factorization theorems for some spaces of analytic functions

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