Factorization of the Fock-Sobolev space

It is well known that polynomially growing/decaying weights come into play in the study of Fock-Sobolev spaces. Given an integer m we introduce the weighted Fock spaces Fpm that contain all entire functions f such that (1 + |z|)(m)f (z) ? Fp. For a positive integer m we have P-m . F-m(p) = F-p and P-m . F-p = F-p-m, where Pm is the ring of all polynomials q(z) on C satisfying deg (q) = m.