1 (p1): Chapter 1.Some Classical Theorems 1 (p1-1): 1.1.The Riesz-Thorin Theorem 5 (p1-2): 1.2.Applications of the Riesz-Thorin Theorem 6 (p1-3): 1.3.The Marcinkiewicz Theorem 11 (p1-4): 1.4.An Application of the Marcinkiewicz Theorem 12 (p1-5): 1.5.Two Classical Approximation Results 13 (p1-6): 1.6.Exercises 19 (p1-7): 1.7.Notes and Comment 22 (p2): Chapter 2.General Properties of Interpolation Spaces 22 (p2-1): 2.1.Categories and Functors 23 (p2-2): 2.2.Normed Vector Spaces 24 (p2-3): 2.3.Couples of Spaces 26 (p2-4): 2.4.Definition of Interpolation Spaces 29 (p2-5): 2.5.The Aronszajn-Gagliardo Theorem 31 (p2-6): 2.6.A Necessary Condition for Interpolation 32 (p2-7): 2.7.A Duality Theorem 33 (p2-8): 2.8.Exercises 36 (p2-9): 2.9.Notes and Comment 38 (p3): Chapter 3.The Real Interpolation Method 38 (p3-1): 3.1.The K-Method 42 (p3-2): 3.2.The J-Method 44 (p3-3): 3.3.The Equivalence Theorem 46 (p3-4): 3.4.Simple Properties of? 48 (p3-5): 3.5.The Reiteration Theorem 52 (p3-6): 3.6.A Formula for the K-Functional 53 (p3-7): 3.7.The Duality Theorem 55 (p3-8): 3.8.A Compactness Theorem 57 (p3-9): 3.9.An Extremal Property of the Real Method 59 (p3-10): 3.10.Quasi-Normed Abelian Groups 63 (p3-11): 3.11.The Real Interpolation Method for Quasi-Normed Abelian Groups 70 (p3-12): 3.12.Some Other Equivalent Real Interpolation Methods 75 (p3-13): 3.13.Exercises 82 (p3-14): 3.14.Notes and Comment 87 (p4): Chapter 4.The Complex Interpolation Method 87 (p4-1): 4.1.Definition of the Complex Method 91 (p4-2): 4.2.Simple Properties of ? 93 (p4-3): 4.3.The Equivalence Theorem 96 (p4-4): 4.4.Multilinear Interpolation 98 (p4-5): 4.5.The Duality Theorem 101 (p4-6): 4.6.The Reiteration Theorem 102 (p4-7): 4.7.On the Connection with the Real Method 104 (p4-8): 4.8.Exercises 105 (p4-9): 4.9.Notes and Comment 106 (p5): Chapter...

zlibzh/no-category/J.BERGH，J.LOFSTROM著, ( )J.Bergh, ()J.Lofstrom著, Rgh Be, Fstrom Lo, J. Bergh, J. Lofstrom著, Rgh Be, Fstrom Lo, Jöran Bergh/插值空间引论_44480547.pdf

Interpolation Spaces: An Introduction (Grundlehren der mathematischen Wissenschaften)

Jöran Bergh, Jörgen Löfström

Joran Bergh; Jorgen Lofstrom

Springer Spektrum. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

World Publishing Corporation

Springer Berlin Heidelberg

世界图书出版公司北京公司

Copernicus

Telos

Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Berlin, 1976

Grundlehren der mathematischen Wissenschaften -- 223 Einzeldarstellungen, 223, Berlin, West Berlin, 1976

Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Reprint, Berlin, 2003

Grundlehren der mathematischen Wissenschaften ;, 223, Berlin, New York, West Berlin, 1976

Springer Nature, Berlin, Heidelberg, 2012

United States, United States of America

China, People's Republic, China

Ying yin ban, Beijing, 2003

Softcover reprint of, 1976

Di 1 ban, Beijing, 2003

Germany, Germany

Dec 20, 1976

Bookmarks: p1 (p1): Chapter 1．Some Classical Theorems
p1-1 (p1): 1.1．The Riesz-Thorin Theorem
p1-2 (p5): 1.2．Applications of the Riesz-Thorin Theorem
p1-3 (p6): 1.3．The Marcinkiewicz Theorem
p1-4 (p11): 1.4．An Application of the Marcinkiewicz Theorem
p1-5 (p12): 1.5．Two Classical Approximation Results
p1-6 (p13): 1.6．Exercises
p1-7 (p19): 1.7．Notes and Comment
p2 (p22): Chapter 2．General Properties of Interpolation Spaces
p2-1 (p22): 2.1．Categories and Functors
p2-2 (p23): 2.2．Normed Vector Spaces
p2-3 (p24): 2.3．Couples of Spaces
p2-4 (p26): 2.4．Definition of Interpolation Spaces
p2-5 (p29): 2.5．The Aronszajn-Gagliardo Theorem
p2-6 (p31): 2.6．A Necessary Condition for Interpolation
p2-7 (p32): 2.7．A Duality Theorem
p2-8 (p33): 2.8．Exercises
p2-9 (p36): 2.9．Notes and Comment
p3 (p38): Chapter 3．The Real Interpolation Method
p3-1 (p38): 3.1．The K-Method
p3-2 (p42): 3.2．The J-Method
p3-3 (p44): 3.3．The Equivalence Theorem
p3-4 (p46): 3.4．Simple Properties of？
p3-5 (p48): 3.5．The Reiteration Theorem
p3-6 (p52): 3.6．A Formula for the K-Functional
p3-7 (p53): 3.7．The Duality Theorem
p3-8 (p55): 3.8．A Compactness Theorem
p3-9 (p57): 3.9．An Extremal Property of the Real Method
p3-10 (p59): 3.10．Quasi-Normed Abelian Groups
p3-11 (p63): 3.11．The Real Interpolation Method for Quasi-Normed Abelian Groups
p3-12 (p70): 3.12．Some Other Equivalent Real Interpolation Methods
p3-13 (p75): 3.13．Exercises
p3-14 (p82): 3.14．Notes and Comment
p4 (p87): Chapter 4．The Complex Interpolation Method
p4-1 (p87): 4.1．Definition of the Complex Method
p4-2 (p91): 4.2．Simple Properties of ？
p4-3 (p93): 4.3．The Equivalence Theorem
p4-4 (p96): 4.4．Multilinear Interpolation
p4-5 (p98): 4.5．The Duality Theorem
p4-6 (p101): 4.6．The Reiteration Theorem
p4-7 (p102): 4.7．On the Connection with the Real Method
p4-8 (p104): 4.8．Exercises
p4-9 (p105): 4.9．Notes and Comment
p5 (p106): Chapter 5．Interpolation of Lp-Spaces
p5-1 (p106): 5.1．Interpolation of Lp-Spaces：the Complex Method
p5-2 (p108): 5.2．Interpolation of Lp-Spaces：the Real Method
p5-3 (p113): 5.3．Interpolation of Lorentz Spaces
p5-4 (p114): 5.4．Interpolation of Lp-Spaces with Change of Measure：p0=p1
p5-5 (p119): 5.5．Interpolation of Lp-Spaces with Change of Measure：p0≠p1
p5-6 (p121): 5.6．Interpolation of Lp-Spaces of Vector-Valued Sequences
p5-7 (p124): 5.7．Exercises
p5-8 (p128): 5.8．Notes and Comment
p6 (p131): Chapter 6．Interpolation of Sobolev and Besov Spaces
p6-1 (p131): 6.1．Fourier Multipliers
p6-2 (p139): 6.2．Definition of the Sobolev and Besov Spaces
p6-3 (p146): 6.3．The Homogeneous Sobolev and Besov Spaces
p6-4 (p149): 6.4．Interpolation of Sobolev and Besov Spaces
p6-5 (p153): 6.5．An Embedding Theorem
p6-6 (p155): 6.6．A Trace Theorem
p6-7 (p156): 6.7．Interpolation of Semi-Groups of Operators
p6-8 (p161): 6.8．Exercises
p6-9 (p169): 6.9．Notes and Comment
p7 (p174): Chapter 7．Applications to Approximation Theory
p7-1 (p174): 7.1．Approximation Spaces
p7-2 (p179): 7.2．Approximation of Functions
p7-3 (p181): 7.3．Approximation of Operators
p7-4 (p182): 7.4．Approximation by Difference Operators
p7-5 (p186): 7.5．Exercises
p7-6 (p193): 7.6．Notes and Comment
p8 (p196): References
p9 (p205): List of Symbols
p10 (p206): Subject Index

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'The works of Jaak Peetre constitute the main body of this treatise.' - preface.

Bibliography: p. [196]-204.
Includes index.

The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu­ script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.

Jöran Bergh, Jörgen Löfström. Includes Index. Bibliography: P. [196]-204.

2024-06-13