Introduction to Hp spaces

Paul Koosis

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.

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  • 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.

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書名 Introduction to Hp spaces
著作者等 Khavin, Viktor Petrovich
Koosis, Paul
シリーズ名 Cambridge tracts in mathematics
出版元 Cambridge University Press
刊行年月 2008
版表示 2nd ed., corr. and augm. with two appendices by V.P. Havin
ページ数 xiv, 287 p.
大きさ 23 cm
ISBN 9780521056816
NCID BB01026408
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言語 英語
出版国 イギリス