Extremal problems in interpolation theory, WhitneyBesicovitch coverings, and singular integrals
 Author/Creator
 Kislyakov, Sergey.
 Language
 English.
 Imprint
 Basel [Switzerland] ; New York : Birkhäuser, c2013.
 Physical description
 x, 316 p. : ill. (some col.) ; 24 cm.
 Series
 Monografie matematyczne ; new ser., v. 74.
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QA281 .K57 2013

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QA281 .K57 2013
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Contributors
 Contributor
 Kruglyak, Natan.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 305311) and index.
 Contents

 Preface. Introduction. Definitions, notation, and some standard facts. Part 1. Background. Chapter 1. Classical CalderonZygmund 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 nearminimizers. Chapter 10. Stability of nearminimizers. Chapter 11. The omitted case of a limit exponent. Chapter A. Appendix. Nearminimizers for Brudnyi and TriebelLizorkin spaces. Notes and remarks. Bibliography. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 In this book we suggest a unified method of constructing nearminimizers for certain important functionals arising in approximation, harmonic analysis and illposed problems and most widely used in interpolation theory. The constructions are based on farreaching refinements of the classical CalderonZygmund decomposition. These new CalderonZygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical results established by Besicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain nearminimizers) under the action of CalderonZygmund 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 selfcontained presentation of the main topic. There we discuss the classical covering results mentioned above, various spectacular applications of the classical CalderonZygmund 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Sergey Kislyakov, Natan Kruglyak.
 Series
 Monografie matematyczne ; new ser., v. 74
 ISBN
 9783034804684
 3034804687