Hardy Martingales: Stochastic Holomorphy, L^1-Embeddings, and Isomorphic Invariants

ISBN-13: 9781108838672 / Angielski / Twarda / 2022 / 500 str.

Paul F. X. Müller (Johannes Kepler Universität Linz)

Opis

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.

Recenzje

'This book presents a wonderful bridge between Probability Theory, Functional Analysis and Complex Analysis, that emerged in last decades due to the work of many great mathematicians. It is a pleasure to read. The results are placed in their logical context and connections between them are clearly explained. Many remarks put the development of the subject into historical perspective. The presentation is clear and reasonably detailed.' Przemysław Wojtaszczyk, IMPAN Warsaw

Spis treści

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.