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Hardy Martingales
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.
Isomorphisms Between H1 Spaces
This book gives a thorough and self contained presentation of H1, its known isomorphic invariants and a complete classification of H1 on spaces of homogeneous type. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals.
Hardy Martingales
This book presents the probabilistic methods around Hardy martingales for applications to complex, harmonic, and functional analysis.
Geometry of Banach Spaces
This volume reflects the progress made in many branches of recent research in Banach space theory. It is based on a conference attended by most of the leading figures in the area, and is intended to illustrate the interplay of Banach space theory with harmonic analysis, probability, complex function theory and finite dimensional convexity theory. The papers consist of a selection of surveys and original research papers. Research workers in functional and complex analysis will find much here to interest them.
Geometric Aspects of Functional Analysis
The scope of the Israel seminar in geometric aspects of functional analysis during the academic year 89/90 was particularly wide covering topics as diverse as: Dynamical systems, Quantum chaos, Convex sets in Rn, Harmonic analysis and Banach space theory. The large majority of the papers are original research papers.
Shift-invariant Uniform Algebras on Groups
This book on the theory of shift-invariant algebras is the first monograph devoted entirely to an outgrowth of the established theory of generalized analytic functions on compact groups. Associated subalgebras of almost periodic functions of real variables and of bonded analytic functions on the unit disc are carried along within the general framework.
Mathematical Reviews
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