Theory of Bergman Spaces

Preliminary Text. Do not use. 15 years ago the function theory and operator theory connected with the Hardy spaces was well understood (zeros; factorization; interpolation; invariant subspaces; Toeplitz and Hankel operators, etc.). None of the techniques that led to all the information about Hardy spaces worked on their close relatives the Bergman spaces. Most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unli