Embeddings and Extensions in Analysis

I. Isometric Embedding.- 1. Introduction.- 2. Isometric Embedding in Hilbert Space.- 3. Functions of Negative Type.- 4. Radial Positive Definite Functions.- 5. A Characterization of Subspaces of Lp, 1 ? p ? 2.- II. The Classes N(X) and RPD(X): Integral Representations.- 6. Radial Positive Definite Functions on ?n.- 7. Positive Definite Functions on Infinite-Dimensional Linear Spaces.- 8. Functions of Negative Type on Lp Spaces.- 9. Functions of Negative Type on ?N.- III. The Extension Problem for Contractions and Isometries.- 10. Formulation.- 11. The Kirszbraun Intersection Property.- 12. Extension of Contractions for Pairs of Banach Spaces.- 13. Special Extension Problems.- IV. Interpolation and Lp Inequalities.- 14. A Multi-Component Riesz-Thorin Theorem.- 15. Lp Inequalities.- 16. A Packing Problem in Lp.- V. The Extension Problem for Lipschitz-Holder Maps between Lp Spaces.- 17. K-Functions and an Extension Procedure for Bilinear Forms.- 18. Examples of K-Functions.- 19. The Contraction Extension Problem for the Pairs (L?q,Lp).- Author Index.- List of Symbols.