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The Resource Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)
Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)
Resource Information
The item Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 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 nearminimizers) 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 selfcontained 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
 Language

 eng
 eng
 Edition
 1st ed. 2013.
 Extent
 1 online resource (319 p.)
 Note
 Description based upon print version of record
 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 nearminimizers
 Chapter 10. Stability of nearminimizers
 Chapter 11. The omitted case of a limit exponent
 Chapter A. Appendix. Nearminimizers for Brudnyi and Triebel–Lizorkin spaces
 Notes and remarks
 Bibliography
 Index
 Isbn
 9781283909945
 Label
 Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals
 Title
 Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals
 Statement of responsibility
 by Sergey Kislyakov, Natan Kruglyak
 Language

 eng
 eng
 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 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 nearminimizers) 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 selfcontained 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
 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, WhitneyBesicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)
 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 nearminimizers  Chapter 10. Stability of nearminimizers  Chapter 11. The omitted case of a limit exponent  Chapter A. Appendix. Nearminimizers 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
 10.1007/9783034804691
 Specific material designation
 remote
 System control number

 (CKB)2670000000279830
 (EBL)1082164
 (OCoLC)819631473
 (SSID)ssj0000798613
 (PQKBManifestationID)11518137
 (PQKBTitleCode)TC0000798613
 (PQKBWorkID)10754616
 (PQKB)11045796
 (DEHe213)9783034804691
 (MiAaPQ)EBC1082164
 (EXLCZ)992670000000279830
 Label
 Extremal Problems in Interpolation Theory, WhitneyBesicovitch Coverings, and Singular Integrals, by Sergey Kislyakov, Natan Kruglyak, (electronic resource)
 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 nearminimizers  Chapter 10. Stability of nearminimizers  Chapter 11. The omitted case of a limit exponent  Chapter A. Appendix. Nearminimizers 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
 10.1007/9783034804691
 Specific material designation
 remote
 System control number

 (CKB)2670000000279830
 (EBL)1082164
 (OCoLC)819631473
 (SSID)ssj0000798613
 (PQKBManifestationID)11518137
 (PQKBTitleCode)TC0000798613
 (PQKBWorkID)10754616
 (PQKB)11045796
 (DEHe213)9783034804691
 (MiAaPQ)EBC1082164
 (EXLCZ)992670000000279830
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