Rademacher System in Function Spaces

• Rademacher functions in L_p-spaces.- The Rademacher system in symmetric spaces situated "far" from L_\infty.- The Rademacher system in symmetric spaces situated "close" to L_\infty.- Rademacher sums with vector coefficients.- Best constants in the Khintchine and Kahane-Khintchine inequalities.- The Rademacher chaos in symmetric spaces.- The comparison of systems of random variables.- The extraction of lacunary subsystems.- Extreme properties of the Rademacher system.- Bernoulli processes.- Rademacher multiplicator spaces.- Some versions of the Khintchine inequality.- Martingale transforms of the Rademacher sequence in symmetric spaces.- Rademacher functions in BMO and Paley spaces.- Rademacher functions in Cesaro type spaces.- Rademacher functions in Morrey spaces.- Appendix A. Some preliminaries from probability theory.- Appendix B. Basic sequences and lacunary systems.- Appendix C. Banach function lattices and symmetric spaces.- Appendix D. Interpolation of operators and spaces of the real method of interpolation.

“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)