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

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 Caldero...

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Détails bibliographiques
Cote:Libro Electrónico
Auteurs principaux: Kislyakov, Sergey (Auteur), Kruglyak, Natan (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
Édition:1st ed. 2013.
Collection:Monografie Matematyczne, 74
Sujets:
Functions of real variables.
Approximation theory.
Functional analysis.
Real Functions.
Approximations and Expansions.
Functional Analysis.
Accès en ligne:Texto Completo
Table des matières:
  • 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.

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