A sharp form of Whitney’s extension theorem

Abstract

3. Order relations involving multi-indices 4. Statement of two main lemmas 5. Plan of the proof 6. Starting the main induction 7. Nonmonotonic sets 8. A consequence of the main inductive assumption 9. Setup for the main induction 10. Applying Helly's theorem on convex sets 11. A Calder6n-Zygmund decomposition 12. Controlling auxiliary polynomials I 13. Controlling auxiliary polynomials II 14. Controlling the main polynomials 15. Proof of Lemmas 9.1 and 5.2 16. A rescaling lemma 17. Proof of Lemma 5.3 18. Proofs of the theorems 19. A bound for k# References