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Representation theorems in Hardy spaces. (English) Zbl 1169.22001
London Mathematical Society Student Texts 74. Cambridge: Cambridge University Press (ISBN 978-0-521-73201-7/pbk; 978-0-521-51768-3/hbk). xii, 372 p. (2009).
This self-contained text provides an introduction to a wide range of representation theorems and gives a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane. With over 300 exercises, many with accompanying hints, this book is ideal for those studying advanced complex analysis, function theory, or the theory of Hardy spaces. Advanced undergraduate and graduate students will find the book easy to follow, with a logical progression from basic theory to advanced research.

MSC:
22-02 Research exposition (monographs, survey articles) pertaining to topological groups
42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
43-02 Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis
42B30 \(H^p\)-spaces
30D55 \(H^p\)-classes (MSC2000)
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