A Factoring Theorem for The Bergman Space

0. Introduction Let D be the open unit disk in the complex plane C, T the unit circle, and L(D) the Bergman space, consisting of those analytic functions on D that are square integrable on D with respect to area measure. The Bergman space is a closed subspace of the Hilbert space L(O) of all square area-integrable complex-valued functions on D. The inner product in L(D), and hence in L(D), is given by the formula f L*= J{z)g(z)dA(z), /geL(D), Jo where dA denotes planar area measure, normalized so that D has total mass 1. The associated norm is denoted by || • ||L2. The Hardy space 77 (B) consists of all functions /holomorphic on O satisfying