Review From the reviews: "After having been out of print for many years, the long-awaited revised first edition of this wonderful book has finally reappeared, this time with Springer Verlag. In 2003, Garnett was awarded the AMS Steel prize for this book; one of the highest distinctions for mathematical exposition. … To sum up, Garnett’s book is as useful now as it was in 1981 and is highly recommended to everyone interested in function theory." (Raymond Mortini, Zentralblatt MATH, Vol. 1106 (8), 2007) "The book contains information about Hardy spaces, conjugate functions, bounded mean oscillation and duality, interpolating sequences, corona construction, Douglas algebras and many other topics. … The book … is a gold mine for researchers and experts." (EMS Newsletter, September, 2008) Read more From the Back Cover The book, which covers a wide range of beautiful topics in analysis, is extremely well organized and well written, with elegant, detailed proofs. The book has educated a whole generation of mathematicians with backgrounds in complex analysis and function algebras. It has had a great impact on the early careers of many leading analysts and has been widely adopted as a textbook for graduate courses and learning seminars in both the US and abroad. - From the Citation for the 2003 Leroy P. Steele Prize for Exposition The author has not attempted to produce a compendium. Rather, he has selected a range of topics in a many-faceted theory and, within that range, penetrated to considerable depth...the author has succeeded in bringing out the beauty of a theory which, despite its relatively advanced age---now approaching 80 years---continues to surprise and to delight its practitioners. The author has left his mark on the subject. - Donald Sarason, Mathematical Reviews Garnett's Bounded Analytic Functions is to function theory as Zygmund's Trigonometric Series is to Fourier analysis. Bounded Analytic Functions is widely regarded as a classic textbook used around the world to educate today's practioners in the field, and is the primary source for the experts. It is beautifully written, but intentionally cannot be read as a novel. Rather it gives just the right level of detail so that the motivated student develops the requisite skills of the trade in the process of discovering the beauty of the combination of real, complex and functional analysis. - Donald E. Marshall, University of Washington Read more
R**D
The best function-space reference.
The study of spaces of holomorphic functions brings together techniques of complex function theory, real analysis, harmonic analysis, and functional analysis. Anyone engaged in this study should have a copy of this book, which does an excellent job of laying out the subject from all of these perspectives. The main body of the text serves as an excellent reference, and the exercises add much more. As far as this reviewer can tell, the book is cited more often in the literature than any other book on the subject. The only problem is that the book is out of print. The reviewer's (faint) hope is that this review will help convince a publisher to republish the book.
V**M
very good
I love the delivery service. I have not had a chance to read the book yet but the condition of the book is very nice.
D**Y
Bounded Analytic Functions
The book is a little turse. The author could have included more details in the proofs.
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