The Resource Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)

Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)

Label
Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals
Title
Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals
Statement of responsibility
by Sergey Kislyakov, Natan Kruglyak
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
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 results established by Besicovitch, 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
Member of
http://library.link/vocab/creatorName
Kislyakov, Sergey
Dewey number
515.2433
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 1RmrM_FjbtQ
  • mJIM3ytZbKs
Language note
English
LC call number
QA331.5
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Kruglyak, Natan.
Series statement
  • Monografie matematyczne
  • Monografie Matematyczne,
Series volume
  • v. 74
  • 74
http://library.link/vocab/subjectName
  • Mathematics
  • Functional analysis
  • Real Functions
  • Approximations and Expansions
  • Functional Analysis
Label
Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (319 p.)
Form of item
online
Isbn
9781283909945
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-0348-0469-1
Specific material designation
remote
System control number
  • (CKB)2670000000279830
  • (EBL)1082164
  • (OCoLC)819631473
  • (SSID)ssj0000798613
  • (PQKBManifestationID)11518137
  • (PQKBTitleCode)TC0000798613
  • (PQKBWorkID)10754616
  • (PQKB)11045796
  • (DE-He213)978-3-0348-0469-1
  • (MiAaPQ)EBC1082164
  • (EXLCZ)992670000000279830
Label
Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (319 p.)
Form of item
online
Isbn
9781283909945
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-0348-0469-1
Specific material designation
remote
System control number
  • (CKB)2670000000279830
  • (EBL)1082164
  • (OCoLC)819631473
  • (SSID)ssj0000798613
  • (PQKBManifestationID)11518137
  • (PQKBTitleCode)TC0000798613
  • (PQKBWorkID)10754616
  • (PQKB)11045796
  • (DE-He213)978-3-0348-0469-1
  • (MiAaPQ)EBC1082164
  • (EXLCZ)992670000000279830

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