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插值空间引论【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

J.BERGH，J.LOFSTROM著著
出版社：北京;西安：世界图书出版公司
ISBN：7506260115
出版时间：2003
标注页数：207页
文件大小：19MB
文件页数：220页
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图书目录

Chapter 1．Some Classical Theorems1

1.1．The Riesz-Thorin Theorem1

1.2．Applications of the Riesz-Thorin Theorem5

1.3．The Marcinkiewicz Theorem6

1.4．An Application of the Marcinkiewicz Theorem11

1.5．Two Classical Approximation Results12

1.6．Exercises13

1.7．Notes and Comment19

Chapter 2．General Properties of Interpolation Spaces22

2.1．Categories and Functors22

2.2．Normed Vector Spaces23

2.3．Couples of Spaces24

2.4．Definition of Interpolation Spaces26

2.5．The Aronszajn-Gagliardo Theorem29

2.6．A Necessary Condition for Interpolation31

2.7．A Duality Theorem32

2.8．Exercises33

2.9．Notes and Comment36

Chapter 3．The Real Interpolation Method38

3.1．The K-Method38

3.2．The J-Method42

3.3．The Equivalence Theorem44

3.4．Simple Properties of？46

3.5．The Reiteration Theorem48

3.6．A Formula for the K-Functional52

3.7．The Duality Theorem53

3.8．A Compactness Theorem55

3.9．An Extremal Property of the Real Method57

3.10．Quasi-Normed Abelian Groups59

3.11．The Real Interpolation Method for Quasi-Normed Abelian Groups63

3.12．Some Other Equivalent Real Interpolation Methods70

3.13．Exercises75

3.14．Notes and Comment82

Chapter 4．The Complex Interpolation Method87

4.1．Definition of the Complex Method87

4.2．Simple Properties of ？91

4.3．The Equivalence Theorem93

4.4．Multilinear Interpolation96

4.5．The Duality Theorem98

4.6．The Reiteration Theorem101

4.7．On the Connection with the Real Method102

4.8．Exercises104

4.9．Notes and Comment105

Chapter 5．Interpolation of Lp-Spaces106

5.1．Interpolation of Lp-Spaces：the Complex Method106

5.2．Interpolation of Lp-Spaces：the Real Method108

5.3．Interpolation of Lorentz Spaces113

5.4．Interpolation of Lp-Spaces with Change of Measure：p0=p1114

5.5．Interpolation of Lp-Spaces with Change of Measure：p0≠p1119

5.6．Interpolation of Lp-Spaces of Vector-Valued Sequences121

5.7．Exercises124

5.8．Notes and Comment128

Chapter 6．Interpolation of Sobolev and Besov Spaces131

6.1．Fourier Multipliers131

6.2．Definition of the Sobolev and Besov Spaces139

6.3．The Homogeneous Sobolev and Besov Spaces146

6.4．Interpolation of Sobolev and Besov Spaces149

6.5．An Embedding Theorem153

6.6．A Trace Theorem155

6.7．Interpolation of Semi-Groups of Operators156

6.8．Exercises161

6.9．Notes and Comment169

Chapter 7．Applications to Approximation Theory174

7.1．Approximation Spaces174

7.2．Approximation of Functions179

7.3．Approximation of Operators181

7.4．Approximation by Difference Operators182

7.5．Exercises186

7.6．Notes and Comment193

References196

List of Symbols205

Subject Index206