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The first edition of this well-known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). This second edition retains many of the features found in the first--detailed computation, an emphasis on methods--but greatly extends its coverage. The discussions of conformal mapping now include Lindelöf's second theorem and the one due to Kellogg. A simple derivation of the atomic decomposition for RH1 is given, and then used to provide an alternative proof of Fefferman's duality theorem. Two appendices by V.P. Havin have also been added: on Peter Jones' interpolation formula for RH1 and on Havin's own proof of the weak sequential completeness of L1/H1(0). Numerous other additions, emendations and corrections have been made throughout.Read more
- First edition well known and well received
- Clear and accessible treatment
- Well illustrated
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"The author's lucid and highly individualistic style succeeds wonderfully in conveying the beauty and depth of a most fascinating area of classical analysis." Mathematical Reviews
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- Edition: 2nd Edition
- Date Published: January 1999
- format: Hardback
- isbn: 9780521455213
- length: 304 pages
- dimensions: 229 x 152 x 21 mm
- weight: 0.62kg
- contains: 73 b/w illus. 10 exercises
- availability: Available
Table of Contents
Preface to the first edition
2. Theorem of the brothers Reisz. Introduction to the space H1
3. Elementary boundary behaviour theory for analytic functions
4. Application of Jensen's formula. Factorisation into a product of inner and outer functions
5. Norm inequalities for harmonic conjugation
6. Hp spaces for the upper half plane
7. Duality for Hp spaces
8. Application of the Hardy-Littlewood maximal function
10. Functions of bounded mean oscillation
11. Wolff's proof of the Corona theorem
Appendix I. Jones' interpolation formula
Appendix II. Weak completeness of the space L1/H1(0)
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