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Field name	Details
Dewey Class	515.8
Title	Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals ([EBook]) / by Sergey Kislyakov, Natan Kruglyak.
Author	Kislyakov, Sergey
Added Personal Name	Kruglyak, Natan
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser
Publication	, 2013.
Physical Details	X, 316 pages. 11 illus., 8 illus. in color. : online resource.
Series	Monografie Matematyczne ; 74
ISBN	9783034804691
Summary Note	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 CalderÃ³nâZygmund decomposition. These new CalderÃ³nâZygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical resultsÂ established byÂ Besicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of CalderÃ³nâZygmund 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 CalderÃ³nâZygmund 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 note	Preface -- Introduction -- Definitions, notation, and some standard facts -- Part 1. Background -- Chapter 1. Classical CalderÃ³nâZygmund 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 TriebelâLizorkin spaces -- Notes and remarks -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0469-1
Links to Related Works	Subject References: Approximations and Expansions . Functional Analysis . Mathematics . Real Functions . Authors: author . Kislyakov, Sergey . Kruglyak, Natan . Corporate Authors: SpringerLink (Online service) . Series: Monografie Matematyczne . Classification: 515.8 . 515.8 (DDC 23) .

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

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