Isomorphisms Between H1 Spaces

This book gives a thorough and self contained presentation of H¹, its known isomorphic invariants and a complete classification of H¹ on spaces of homogeneous type. 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. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals.

List of contents

The Haar System: Basic Facts and Classical Results.- Projections, Isomorphisms and Interpolation.- Combinatorics of Colored Dyadic Intervals.- Martingale H1 Spaces.- Isomorphic Invariants for H1.- Atomic H1 Spaces.

Summary

This book gives a thorough and self contained presentation of H¹, its known isomorphic invariants and a complete classification of H¹ on spaces of homogeneous type. 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. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals.

Additional text

"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)

Product details

• Authors: Paul F X Müller, Paul F. X. Müller, Paul F.X. Müller
• Publisher: Springer, Basel
• Languages: English
• Product format: Hardback
• Released: 19.07.2005
• EAN: 9783764324315
• ISBN: 978-3-7643-2431-5
• No. of pages: 453
• Weight: 1194 g
• Illustrations: XIV, 453 p.
• Series: Monografie Matematyczne; Monografie Matematyczne
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, Stochastik, B, Mathematics and Statistics, Functional Analysis, Probability Theory and Stochastic Processes, Probability & statistics, Complex analysis, complex variables, Abstract Harmonic Analysis, Harmonic analysis, Probabilities, Stochastics, Probability Theory, Analysis (Mathematics), Functional analysis & transforms, Mathematical analysis