Theory of Bergman Spaces

15 years ago the function theory and operator theory connected with th e Hardy spaces was well understood (zeros; factorization; interpolatio n; invariant subspaces; Toeplitz and Hankel operators, etc.). None of the techniques that led to all the information about Hardy spaces work ed on their close relatives the Bergman spaces. Most mathematicians wh o worked in the intersection of function theory and operator theory th ought that progress on the Bergman spaces was unlikely. Now the situat ion has completely changed. Today there are rich theories describing t he Bergman spaces and their operators. Research interest and research activity in the area has been high for several years. A book is badly needed on Bergman spaces and the three authors are the right people to write it.