Extremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals Sergey Kislyakov, Natan Kruglyak

Format:

Book

Author/Creator:

Kislyakov, Sergey

Contributor:

Kruglyak, Natan

Series:

Monografie matematyczne v. 74

Language:

English

Subjects (All):

Interpolation.

Interpolation spaces.

Physical Description:

1 online resource

Place of Publication:

New York Springer 2013

Summary:

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 Calderón-Zygmund decomposition. These new Calderón-Zygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical resultsestablished byBesicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of Calderón-Zygmund singular integral operators. The book is divided into two parts. While the new method is presented in great detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic. There we discuss the classical covering results mentioned above, various spectacular applications of the classical Calderón-Zygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quick introduction to such important topics as spaces of smooth functions or singular integrals

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

Notes:

Includes bibliographical references and index

Other Format:

Print version Kislyakov, Sergey. Extremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals

ISBN:

9783034804691

3034804695

3034804687

9783034804684

OCLC:

823741699

Access Restriction:

Restricted for use by site license