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

This book provides 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. Offering a comprehensive reference guide to the subject, it is the first of its kind in this area. After several introductory chapters covering the basic material, a large variety of results obtained over the past 80 years, including the most recent ones, are treated in detail.

Several chapters end with discussions of 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 value in their own work. The book can also be used as a textbook or a supplementary reference for an advanced graduate course. It is primarily intended for specialists in complex and functional analysis, graduate students, and experts in other related fields.

1 Basic Spaces. Multipliers. - 2 The Poisson Integral. - 3 Subharmonic and h-subharmonic Functions. - 4 Hardy Spaces of Analytic Functions. - 5 Carleson Measures, Mean Oscillation Spaces and Duality. - 6 Polynomial Approximation and Taylor Coefficients of Hp Functions. - 7 The Mixed Norm Spaces Hp, q, . - 8 Hp, q, as a Sequence Space. - 9 Tensor Products and Multipliers. - 10 Duality and Multipliers. - 11 Multipliers From Hp and Hp, q, Spaces to s. - 12 Multiplier Spaces (Hp, q, , Hu, v, ß) and (Hp, Hu). - 13 Multipliers of Some Large Spaces of Analytic Functions. - 14 The Hilbert Matrix Operator.