The Rademacher System in Function Spaces

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in L__p__-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces. Front Matter ....Pages i-xx Rademacher Functions in Lp-Spaces (Sergey V. Astashkin)....Pages 1-28 Rademacher System in Symmetric Spaces Located “far” from L∞ (Sergey V. Astashkin)....Pages 29-47 Rademacher System in Symmetric Spaces Located “close” to L∞ (Sergey V. Astashkin)....Pages 49-91 Rademacher Sums with Vector Coefficients (Sergey V. Astashkin)....Pages 93-134 Optimal Constants in the Khintchine Type Inequalities (Sergey V. Astashkin)....Pages 135-161 Rademacher Chaos in Symmetric Spaces (Sergey V. Astashkin)....Pages 163-197 The Comparison of Systems of Random Variables (Sergey V. Astashkin)....Pages 199-228 Extraction of Lacunary Subsystems (Sergey V. Astashkin)....Pages 229-263 Extreme Properties of the Rademacher System (Sergey V. Astashkin)....Pages 265-290 Bernoulli Processes (Sergey V. Astashkin)....Pages 291-310 Rademacher Multiplicator Spaces (Sergey V. Astashkin)....Pages 311-378 Some Versions of Khintchine’s Inequality (Sergey V. Astashkin)....Pages 379-417 Martingale Transforms of the Rademacher Sequence in Symmetric Spaces (Sergey V. Astashkin)....Pages 419-438 Rademacher Functions in BMO and Paley Spaces (Sergey V. Astashkin)....Pages 439-467 Rademacher Functions in the Cesàro Type Spaces (Sergey V. Astashkin)....Pages 469-490 Rademacher Functions in Morrey Spaces (Sergey V. Astashkin)....Pages 491-514 Back Matter ....Pages 515-559 "This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces." -- prové de l'editor This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in L p -spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.