Hardy Martingales

Erscheinungsjahr 2022
ISBN: 978-1-108-83867-2
Verlag: Cambridge University Press

Buch, Englisch, Band 43, 500 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 984 g

Reihe: New Mathematical Monographs

This book presents the probabilistic methods around Hardy martingales for an audience interested in applications to complex, harmonic, and functional analysis. Building on work of Bourgain, Garling, Maurey, Pisier, and Varopoulos, it discusses in detail those martingale spaces that reflect characteristic qualities of complex analytic functions. Its particular themes are holomorphic random variables on Wiener space, and Hardy martingales on the infinite torus product, and their numerous deep applications to the geometry and classification of complex Banach spaces, e.g. the embedding of L1 into L1/H1, the isomorphic classification theorem for the class of poly-disk algebras, or the real variables characterization of Banach spaces with the analytic Radon Nikodym property. Including key background material on stochastic analysis and Banach space theory, it is suitable for a wide spectrum of researchers and graduate students working in classical and functional analysis.

Autoren/Hrsg.

Müller, Paul F. X.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Preface; 1. Stochastic Holomorphy; 2. Hardy Martingales; 3. Embedding L1 in L1=H01; 4. Embedding L1 in X or L1/X 5. Isomorphic Invariants; 6. Operators on Lp(L1); 7. Formative Examples; Bibliography; Notation index; Subject index.