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

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.

Reviews & endorsements

'A beautiful exposition of the holomorphic side of martingale theory, where Hardy martingales play the leading role, with many deep applications to Banach spaces. Unlike most books on martingale theory where convexity is central, Müller's remarkable and unique book places the emphasis on the martingales that arise from averaging the boundary values of analytic functions in Hardy spaces. The latter discretize the continuous martingales obtained by composing an analytic function with complex Brownian motion. Consideration of the Banach space valued case leads to deep geometric applications.' Gilles Pisier, Texas A&M

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Product details

• Date Published: July 2022
• format: Hardback
• isbn: 9781108838672
• length: 500 pages

• dimensions: 235 x 158 x 35 mm
• weight: 0.92kg
• availability: Available