The Rademacher System in Function Spaces
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Beschreibung
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.
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.Uses a wide diversity of methods reflecting the Rademacher system in various areas of mathematics Includes Appendices explaining the prerequisites needed Collects material available only scattered through journal articles so far
Autor*in
Sergey V. Astashkin
Themen in »The Rademacher System in Function Spaces«
Rademacher functions symmetric space Khintchine inequality interpolation of operators Peetre K-functional
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“This is a very interesting and well-written book dedicated to the study of the behavior of the Rademacher functions in Banach function spaces. The presentation of this extensive book (559 pages!) is elegant … . Many results given in the book under review have direct applications in the study of the Banach structure of symmetric function spaces on probability spaces.” (Francisco L. Hernández, Mathematical Reviews, January, 2022)
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