Hardy Martingales Stochastic Holomorphy, L^1-Embeddings, and Isomorphic Invariants New Mathematical Monographs Series

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.

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.

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