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Monografie Matematyczne
cover

Isomorphisms Between H¹ Spaces

Authors: Müller, Paul F.X.

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About this book

This book presents a thorough and self-contained presentation of H¹ and its known isomorphic invariants, such as the uniform approximation property, the dimension conjecture, and dichotomies for the complemented subspaces.
The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it (averaging projections, rearrangement operators, paraproducts, Calderon-Zygmund singular integrals). Complete proofs are given for the classical martingale inequalities of C. Fefferman, Burkholder, and Khinchine-Kahane, and for large deviation inequalities. Complex interpolation, analytic families of operators, and the Calderon product of Banach lattices are treated in the context of H^p spaces.
Througout the book, special attention is given to the combinatorial methods developed in the field, particularly J. Bourgain's proof of the dimension conjecture, L. Carleson's biorthogonal system in H¹, T. Figiel's integral representation, W.B. Johnson's factorization of operators, B. Maurey's isomorphism, and P. Jones' proof of the uniform approximation property. An entire chapter is devoted to the study of combinatorics of colored dyadic intervals.

Reviews

"Ein bedeutendes, in Inhalt und Form vorzügliches Standardwerk über faszinierende, tiefliegende mathematische Probleme vor, zu deren Lösung viele der besten Mathematiker beigetragen haben." (Monatshefte für Mathematik)

Table of contents (6 chapters)

Table of contents (6 chapters)
  • The Haar System: Basic Facts and Classical Results

    Pages 1-115

  • Projections, Isomorphisms and Interpolation

    Pages 117-168

  • Combinatorics of Colored Dyadic Intervals

    Pages 169-228

  • Martingale H1 Spaces

    Pages 229-265

  • Isomorphic Invariants for H1

    Pages 267-346

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-3-7643-7345-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Isomorphisms Between H¹ Spaces
Authors
Series Title
Monografie Matematyczne
Series Volume
66
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7345-0
DOI
10.1007/b137684
Hardcover ISBN
978-3-7643-2431-5
Series ISSN
0077-0507
Edition Number
1
Number of Pages
XIV, 458
Topics