Preliminary Text. Do not use. 15 years ago the function theory and operatortheory connected with the Hardy spaces was well understood zerosfactorization interpo... » 

Preliminary Text. Do not use. 15 years ago the function theory and operatortheory connected with the Hardy spaces was well understood zerosfactorization interpolation invariant subspaces Toeplitz and Hankeloperators etc.. None of the techniques that led to all the information aboutHardy spaces worked on their close relatives the Bergman spaces. Mostmathematicians who worked in the intersection of function theory and operatortheory thought that progress on the Bergman spaces was unlikely. Now thesituation has completely changed. Today there are rich theories describing theBergman spaces and their operators. Research interest and research activity inthe area has been high for several years. A book is badly needed on Bergmanspaces and the three authors are the right people to write it. TOCThe BergmanSpaces. The Berezin Transform. ApInner Functions. Zero Sets for BergmanSpaces. Invariant Subspaces. Interpolation and Sampling. Cyclic Vectors. «