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| Chapter 1. Some Classical Theorems 1.1. The Riesz-Thorin Theorem 1.2. Applications of the Riesz-Thorin Theorem 1.3. The Marcinkiewicz Theorem 1.4. An Application of the Marcinkiewicz Theorem 1.5. Two Classical Approximation Results 1.6. Exercises 1.7. Notes and Comment Chapter 2. General Properties of Interpolation Spaces 2.1. Categories and Functors 2.2. Normed Vector Spaces 2.3. Couples of Spaces 2.4. Definition of Interpolation Spaces 2.5. The Aronszajn-Gagliardo Theorem 2.6. A Necessary Condition for Interpolation 2.7. A Duality Theorem 2.8. Exercises 2.9. Notes and Comment Chapter 3. The Real Interpolation Method 3.1. The K-Method 3.2. The J-Method 3.3. The Equivalence Theorem 3.4. Simple Properties of Ao, q 3.5. The Reiteration Theorem 3.6. A Formula for the K-Functional 3.7. The Duality Theorem 3.8. A Compactness Theorem 3.9. An Extremal Property of the Real Method 3.10. Quasi-Normed Abelian Groups 3.11. The Real Interpolation Method for Quasi-Normed Abelian Groups 3.12. Some Other Equivalent Real Interpolation Methods 3.13. Exercises 3.14. Notes and Comment Chapter 4. The Complex Interpolation Method 4.1. Definition of the Complex Method 4.2. Simple Properties of A[o] 4.3. The Equivalence Theorem 4.4. Multilinear Interpolation 4.5. The Duality Theorem 4.6. The Reiteration Theorem 4.7. On the Connection with the Real Method 4.8. Exercises 4.9. Notes and Comment Chapter 5. Interpolation of Lp-Spaces 5.1. Interpolation of Lp-Spaces: the Complex Method 5.2. Interpolation of Lp-Spaces: the Real Method 5.3. Interpolation of Lorentz Spaces 5.4. Interpolation of Lp-Spaces with Change of Measure: Po =P1 5.5. Interpolation of La-Spaces with Change of Measure: Po ≠P1 5.6. Interpolation of La-Spaces of Vector-Valued Sequences 5.7. Exercises 5.8. Notes and Comment Chapter 6. Interpolation of Sobolev and Besov Spaces 6.1. Fourier Multipliers 6.2. Definition of the Sobolev and Besov Spaces 6.3. The Homogeneous Sobolev and Besov Spaces 6.4. Interpolation of Sobolev and Besov Spaces 6.5. An Embedding Theorem 6.6. A Trace Theorem 6.7. Interpolation of Semi-Groups of Operators 6.8. Exercises 6.9. Notes and Comment Chapter 7. Applications to Approximation Theory 7.1. Approximation Spaces 7.2. Approximation of Functions 7.3. Approximation of Operators 7.4. Approximation by Difference Operators 7.5. Exercises 7.6. Notes and Comment References List of Symbols Subject Index |
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