Introduction to Hp Spaces

This edition has two new appendices by V. P. Havin plus numerous improvements, additions and corrections throughout.

Paul Koosis (Author)

9780521056816, Cambridge University Press

Paperback / softback, published 27 March 2008

304 pages, 73 b/w illus. 10 exercises
22.9 x 15.2 x 1.7 cm, 0.45 kg

"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

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). The intention was to give the reader, assumed to know basic real and complex variable theory and a little functional analysis, a secure foothold in the basic theory, and to understand its applications in other areas. For this reason, emphasis is placed on methods and the ideas behind them rather than on the accumulation of as many results as possible. The second edition retains that intention, but the coverage has been extended. The author has included two appendices by V. P. Havin, on Peter Jones' interpolation formula, and Havin's own proof of the weak sequential completeness of L1/H1(0); in addition, numerous amendments, additions and corrections have been made throughout.

Preface
Preface to the first edition
1. Rudiments
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
9. Interpolation
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)
Bibliography
Index.

Subject Areas: Calculus & mathematical analysis [PBK]