Mobius Invariant QK Spaces

This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller 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. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.

“The book has a comprehensive and up-to-date bibliography, which is a valuable asset to any researcher in the field. … Without a question, the book under review is useful for the student contemplating working in the field. I am also happy to notice that the book has something to offer for researchers at all levels, as it is a thorough and illuminating presentation of the current state of the theory.” (Janne Gröhn, Mathematical Reviews, March, 2018)“This comprehensive monograph summarizes the main results about QK spaces obtained since the beginning of this century. It is reader-friendly, well written, self-contained and well structured. … this book will be useful to researchers interested in this field under active development. Moreover, each chapter ends with a list of exercises and it would be an excellent textbook for advanced students with a good background in real and complex analysis.” (Joan Fàbrega, zbMATH 1387.30001, 2018)

Hasi Wulan is a professor, Ph.D supervisor, and the current Vice President of Shantou University. His research areas are function spaces and theory of operators as well as holomorphic functions of one and several complex variables.Kehe Zhu is a professor in the Department of Mathematics and Statistics at the State University of New York at Albany. His research interests include operators on holomorphic function spaces, complex analysis, and operator theory and operator algebras.