Factorization of the Fock–Sobolev space

Abstract

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 F m p that contain all entire functions f such that ( 1 + | z | ) m f ( z ) ∈ F p . For a positive integer m we have P m ⋅ F m p = F p and P m ⋅ F p = F − m p , where P m is the ring of all polynomials q ( z ) on C satisfying deg ⁡ ( q ) ≤ m .