Factorization for non-nevanlinna classes of analytic functions

A generalization of the Blaschke product is constructed. This product enables one to factor out the zeros of the members of certain non-Nevanlinna classes of functions analytic in the unit disc, so that the remaining (non-vanishing) functions still belong to the same class. This is done for the classes A ^-n (0<n<∞) and B ^-n (0<n<2) defined as follows:f ∈A ^-n iff |f(z)|≦C _f (1-|z|)^-n, f ∈B ^-n iff |f(z)|≦exp {C _f (1-|z|)^-n }, where C _f depends on f.