The Rademacher System in Function Spaces

1. Front Matter

   Pages i-xx

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2. Rademacher Functions in L _p-Spaces

   • Sergey V. Astashkin

   Pages 1-28

3. Rademacher System in Symmetric Spaces Located “far” from L _∞

   • Sergey V. Astashkin

   Pages 29-47

4. Rademacher System in Symmetric Spaces Located “close” to L _∞

   • Sergey V. Astashkin

   Pages 49-91

5. Rademacher Sums with Vector Coefficients

   • Sergey V. Astashkin

   Pages 93-134

6. Optimal Constants in the Khintchine Type Inequalities

   • Sergey V. Astashkin

   Pages 135-161

7. Rademacher Chaos in Symmetric Spaces

   • Sergey V. Astashkin

   Pages 163-197

8. The Comparison of Systems of Random Variables

   • Sergey V. Astashkin

   Pages 199-228

9. Extraction of Lacunary Subsystems

   • Sergey V. Astashkin

   Pages 229-263

10. Extreme Properties of the Rademacher System

    • Sergey V. Astashkin

    Pages 265-290

11. Bernoulli Processes

    • Sergey V. Astashkin

    Pages 291-310

12. Rademacher Multiplicator Spaces

    • Sergey V. Astashkin

    Pages 311-378

13. Some Versions of Khintchine’s Inequality

    • Sergey V. Astashkin

    Pages 379-417

14. Martingale Transforms of the Rademacher Sequence in Symmetric Spaces

    • Sergey V. Astashkin

    Pages 419-438

15. Rademacher Functions in BMO and Paley Spaces

    • Sergey V. Astashkin

    Pages 439-467

16. Rademacher Functions in the Cesàro Type Spaces

    • Sergey V. Astashkin

    Pages 469-490

17. Rademacher Functions in Morrey Spaces

    • Sergey V. Astashkin

    Pages 491-514

18. Back Matter

    Pages 515-559

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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.

• Rademacher functions
• symmetric space
• Khintchine inequality
• interpolation of operators
• Peetre K-functional

“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)

• Samara National Research University, Samara, Russia

  Sergey V. Astashkin

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