Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces

This book aims to provide a systematic overview of the theory of Taylor coefficients of functions in some classical spaces of analytic functions and especially of the coefficient multipliers between spaces of Hardy type. It is intended to serve as a complete reference on the subject and is the first of its kind in this area. After several introductory chapters covering the basic material, a large number of results obtained over the past 80 years or so, up to the most recent ones, are treated in detail. Several chapters end with practical applications and related topics that graduate students and experts in other subjects may find useful for their own purposes. Thus, a further aim of the book is to communicate to non-specialists some concrete facts that may be of interest for their own work. The book can also be used as a text or a supplementary reference for an advanced graduate course. It is addressed to specialists in complex and functional analysis, graduate students, and experts in other related fields.