Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals

• Main Authors: Kislyakov, Sergey (Author), Kruglyak, Natan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
• Series: Monografie Matematyczne ; 74
• Subjects: Mathematics.; Approximation theory.; Functional analysis.; Functions of real variables.; Real Functions.; Approximations and Expansions.; Functional Analysis.

In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. The constructions are based on far-reaching refinements of the classical Calderó...

Table of Contents:

• Preface
• Introduction
• Definitions, notation, and some standard facts
• Part 1. Background
• Chapter 1. Classical Calderón–Zygmund decomposition and real interpolation
• Chapter 2. Singular integrals
• Chapter 3. Classical covering theorems
• Chapter 4. Spaces of smooth functions and operators on them
• Chapter 5. Some topics in interpolation
• Chapter 6. Regularization for Banach spaces
• Chapter 7. Stability for analytic Hardy spaces
• Part 2. Advanced theory
• Chapter 8. Controlled coverings
• Chapter 9. Construction of near-minimizers
• Chapter 10. Stability of near-minimizers
• Chapter 11. The omitted case of a limit exponent
• Chapter A. Appendix. Near-minimizers for Brudnyi and Triebel–Lizorkin spaces
• Notes and remarks
• Bibliography
• Index.