Hardy martingales : stochastic holomorphy, L1-embeddings, and isomorphic invariants / Paul F. X. Müller.

Format:

Book

Author/Creator:

Müller, Paul F. X., author.

Series:

New mathematical monographs ; 43.

New mathematical monographs ; 43

Language:

English

Subjects (All):

Martingales (Mathematics).

Stochastic analysis.

Ideal spaces.

Probabilities.

Physical Description:

1 online resource (xv, 500 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2022.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 01 Jul 2022).

Other Format:

Print version:

ISBN:

9781108976015 (ebook)

Access Restriction:

Restricted for use by site license.