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 SL? 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.
| ISBN: | 9781108838672 |
| Publication date: | 14th July 2022 |
| Author: | Paul F X Müller |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 518 pages |
| Series: | New Mathematical Monographs |
| Genres: |
Mathematics and Science Real analysis, real variables Complex analysis, complex variables Functional analysis and transforms Stochastics |
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 SL? 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.
Hardy Martingales features in the following genres: Mathematics and Science, Real analysis, real variables, Complex analysis, complex variables, Functional analysis and transforms, Stochastics
Hardy Martingales is available in Hardback
Hardy Martingales was written by Paul F X Müller and published by Cambridge University Press
Hardy Martingales has 518 pages
Yes it is part of New Mathematical Monographs series
£117.90