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Multiplicative inequalities of Carlson type and interpolation /
This unique volume contains a selection of more than 80 of Yuval Ne'eman's papers, which represent his huge contribution to a large number of aspects of theoretical physics. The works span more than four decades, from unitary symmetry and quarks to questions of complexity in biological sys...
| Cote: | Libro Electrónico |
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| Autres auteurs: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
New Jersey :
World Scientific,
©2006.
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| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- Preface
- 0. Introduction and notation. 0.1. Notational conventions
- 1. Carlson's inequalities. 1.1. Carlson's proof. 1.2. Hardy's proofs. 1.3. An alternate proof. 1.4. Carlson's inequality for finite sums
- 2. Some extensions and complements of Carlson's inequalities. 2.1. Gabriel. 2.2. Levin. 2.3. Caton. 2.4. Bellman. 2.5. Two discrete Carlson by-products. 2.6. Landau and Levin-Stec̮kin. 2.7. Some extensions of the Landau and Levin-Stec̮kin inequalities. 2.8. Proofs. 2.9. Levin-Godunova. 2.10. More about finite sums
- 3. The continuous case. 3.1. Beurling. 3.2. Kjellberg. 3.3. Bellman. 3.4. Sz. Nagy. 3.5. Klefsjö. 3.6. Hu. 3.7. Yang-Fang. 3.8. A continuous Landau type inequality. 3.9. Integrals on bounded intervals
- 4. Levin's theorem
- 5. Some multi-dimensional generalizations and variations. 5.1. Some preliminaries. 5.2. A sharp inequality for cones in [symbol]. 5.3. Some variations on the multi-dimensional theme. 5.4. Some further generalizations
- 6. Some Carlson type inequalities for weighted Lebesgue spaces with general measures. 6.1. The basic case. 6.2. The product measure case
- two factors. 6.3. The general product measure case
- 7. Carlson type inequalities and real interpolation theory. 7.1. Interpolation of normed spaces. 7.2. The real interpolation method. 7.3. Embeddings of real interpolation spaces
- 8. Further connection to interpolation theory, the Peetre [symbol] method. 8.1. Introduction. 8.2. Carlson type inequalities as sharpenings of Jensen's inequality. 8.3. The Peetre interpolation method and interpolation of Orlicz spaces. 8.4. A Carlson type inequality with blocks. 8.5. The Calderón-Lozanovskiǐ construction on Banach lattices
- 9. Related results and applications. 9.1. A generalization of Redheffer. 9.2. Sobolev type embeddings. 9.3. A local Hausdorff-Young inequality. 9.4. Optimal sampling. 9.5. More on interpolation, the Peetre parameter theorem. 9.6. Carlson type inequalities with several factors. 9.7. Reverse Carlson type inequalities. 9.8. Some further possibilities. 9.9. Necessity in the case of a general measure.