Müller / Muller Hardy Martingales

Stochastic Holomorphy, L^1-Embeddings, and Isomorphic Invariants
Erscheinungsjahr 2022
ISBN: 978-1-108-98596-3
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 43

Reihe: New Mathematical Monographs

This book presents the probabilistic methods around Hardy martingales for an audience interested in their applications to complex, harmonic, and functional analysis. Building on work of Bourgain, Garling, Jones, 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 numerous deep applications to the geometry and classification of complex Banach spaces, e.g., the SL8 estimates for Doob's projection operator, the embedding of L1 into L1/H1, the isomorphic classification theorem for the polydisk algebras, or the real variables characterization of Banach spaces with the analytic Radon Nikodym property. Due to the inclusion of key background material on stochastic analysis and Banach space theory, it's suitable for a wide spectrum of researchers and graduate students working in classical and functional analysis.

Autoren/Hrsg.

Müller, Paul F. X.

Muller, Paul F. X.

Fachgebiete

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

Inhaltsverzeichnis

Preface 1. Stochastic Holomorphy 2. Hardy Martingales 3. Embedding L1 in L1/H1 4. Embedding L1 in X or L1/X 5. Isomorphic Invariants 6. Operators on Lp(L1) 7. Formative Examples Bibliography Notation index Subject index.

Über Autor(innen)

Müller, Paul F. X.
Paul F. X. Müller is Professor at Johannes Kepler University in Linz, Austria. He is the author of over 50 papers in complex, harmonic and functional analysis and of the monograph Isomorphisms between H^1 spaces (Springer, 2005).