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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.

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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 H p Functions.- 7 The Mixed Norm Spaces H p,q, .- 8 H p,q, as a Sequence Space.- 9 Tensor Products and Multipliers.- 10 Duality and Multipliers.- 11 Multipliers From H p and H p,q, Spaces to s .- 12 Multiplier Spaces ( H p,q, ,H u,v,beta ) and ( H p ,H u ).- 13 Multipliers of Some Large Spaces of Analytic Functions.- 14 The Hilbert Matrix Operator.

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Miroljub Jevtic graduated and received his Ph.D. from the University of Belgrade, where he was a Professor of Mathematical Analysis and a Principal Investigator on several research grants until his recent retirement. He has also spent three semesters as a visiting professor at the University of Wisconsin in Madison. He has published over 75 research papers, including 50 in indexed journals. His research involves real, functional, harmonic, and complex analysis (both in one and several variables), primarily in relation to the Hardy and Bergman spaces of analytic functions.

Dragan Vukotic graduated from the University of Belgrade, where he was also a Teaching Assistant, and received his Ph.D. from the University of Michigan, Ann Arbor. After a year at Northwestern University he switched to Universidad Autónoma de Madrid. He was also an adjunct member of the ICMAT Institute in Madrid and a visiting scholar at the Mittag-Leffler Institut. He has been a Principal Investigator on several research grants in Spain. He has authored more than 40 research papers, together with coauthors from various countries, on geometric function theory, spaces of analytic functions, and the operators that act on them.

Milos Arsenovic graduated from the University of Belgrade and received his Ph.D from the University of California, Berkeley. After holding a postdoctoral position at Yale University, he is currently a Professor of Mathematics at the University of Belgrade. Having published more than 30 research papers, his research interests include function spaces, geometric function theory, and harmonic analysis.

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