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Rectifiable measures, square functions involving densities, and the Cauchy transform /
"This monograph is devoted to the proof of two related results. The first one asserts that if is a Radon measure in satisfyingfor -a.e., then is rectifiable. Since the converse implication is already known to hold, this yields the following characterization of rectifiable sets: a set with finit...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2017.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1158. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Chapter 1. Introduction Chapter 2. Preliminaries Chapter 3. A compactness argument Chapter 4. The dyadic lattice of cells with small boundaries Chapter 5. The Main Lemma Chapter 6. The stopping cells for the proofof Main Lemma 5.1 Chapter 7. The measure $\tilde \mu $ and some estimatesabout its flatness Chapter 8. The measure of the cells from $\BCF $, $\LD $, $\BSD $and $\BCG $ Chapter 9. The new families of cells $\bsb $, $\nterm $, $\ngood $, $\nqgood $ and $\nreg $ Chapter 10. The approximating curves $\Gamma ^k$ Chapter 11. The small measure $\tilde \mu $ of the cells from $\bsb $ Chapter 12. The approximating measure $\nu ^k$ on $\Gamma ^k_ex$ Chapter 13. Square function estimates for $\nu ^k$ Chapter 14. The good measure $\sigma ^k$ on $\Gamma ^k$ Chapter 15. The $L^2(\sigma ^k)$ norm of the density of $\nu ^k$ with respect to $\sigma ^k$ Chapter 16. The end of the proof of the Main Lemma 5.1 Chapter 17. Proof of Theorem 1.3: Boundedness of $T_\mu $ implies boundedness of the Cauchy transform Chapter 18. Some Calderón-Zygmund theory for $T_\mu $ Chapter 19. Proof of Theorem 1.3: Boundedness of the Cauchy transform implies boundedness of $T_\mu $