Bücher von Kehe Zhu

Can be used as a graduate textContains many exercisesContains new results

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 unlikely. Now the situation has completely changed. Today there are rich theories describing the 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.

While Hardy and Bergman spaces are established subjects in the literature on analytic functions, Fock spaces remain virgin territory. This book meets the need for a focused presentation of key results and techniques and includes new and simpler proofs.

This monograph summarizes the recent major achievements in Moebius invariant QK spaces. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmuller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis.