The theory of Bergman spaces experienced three main phases of development during the last three decades.
The early 1970's marked the beginning of function theoretic studies in these
spaces. Substantial progress was made by Horowitz and Korenblum, among others,
in the areas of zero sets, cyclic vectors, and invariant subspaces. An influential pre-
presentation of the situation up to the mid 1970's was Shields' survey paper "Weighted
shift operators and analytic function theory".