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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.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1158. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn965547797 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr |n||||||||| | ||
| 008 | 161118t20172016riua ob 000 0 eng d | ||
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| 066 | |c (S | ||
| 019 | |a 1086558741 |a 1262678671 | ||
| 020 | |a 9781470436056 |q (online) | ||
| 020 | |a 1470436051 |q (online) | ||
| 020 | |z 9781470422523 |q (alk. paper) | ||
| 020 | |a 1470422522 |q (alk. paper) | ||
| 020 | |a 9781470422523 | ||
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| 035 | |a (OCoLC)965547797 |z (OCoLC)1086558741 |z (OCoLC)1262678671 | ||
| 050 | 4 | |a QA312 |b .T635 2017 | |
| 082 | 0 | 4 | |a 515/.42 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Tolsa, Xavier, |e author. | |
| 245 | 1 | 0 | |a Rectifiable measures, square functions involving densities, and the Cauchy transform / |c Xavier Tolsa. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2017. | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (v, 130 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 245, number 1158 | |
| 588 | 0 | |a Online resource; title from PDF title page (viewed November 18, 2016). | |
| 500 | |a "Volume 245, Number 1158 (third of 6 numbers), January 2017." | ||
| 504 | |a Includes bibliographical references (pages 129-130). | ||
| 505 | 0 | 0 | |6 880-01 |t Chapter 1. Introduction |t Chapter 2. Preliminaries |t Chapter 3. A compactness argument |t Chapter 4. The dyadic lattice of cells with small boundaries |t Chapter 5. The Main Lemma |t Chapter 6. The stopping cells for the proofof Main Lemma 5.1 |t Chapter 7. The measure $\tilde \mu $ and some estimatesabout its flatness |t Chapter 8. The measure of the cells from $\BCF $, $\LD $, $\BSD $and $\BCG $ |t Chapter 9. The new families of cells $\bsb $, $\nterm $, $\ngood $, $\nqgood $ and $\nreg $ |t Chapter 10. The approximating curves $\Gamma ^k$ |t Chapter 11. The small measure $\tilde \mu $ of the cells from $\bsb $ |t Chapter 12. The approximating measure $\nu ^k$ on $\Gamma ^k_ex$ |t Chapter 13. Square function estimates for $\nu ^k$ |t Chapter 14. The good measure $\sigma ^k$ on $\Gamma ^k$ |t Chapter 15. The $L^2(\sigma ^k)$ norm of the density of $\nu ^k$ with respect to $\sigma ^k$ |t Chapter 16. The end of the proof of the Main Lemma 5.1 |t Chapter 17. Proof of Theorem 1.3: Boundedness of $T_\mu $ implies boundedness of the Cauchy transform |t Chapter 18. Some Calderón-Zygmund theory for $T_\mu $ |t Chapter 19. Proof of Theorem 1.3: Boundedness of the Cauchy transform implies boundedness of $T_\mu $ |
| 520 | 3 | |a "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 finite -dimensional Hausdorff measure is rectifiable if and only if Ĥ1x2E The second result of the monograph deals with the relationship between the above square function in the complex plane and the Cauchy transform . Assuming that has linear growth, it is proved that is bounded in if and only iffor every square ."--Publisher website. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Radon measures. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 0 | |a Cauchy transform. | |
| 650 | 0 | |a Transformations (Mathematics) | |
| 650 | 6 | |a Mesures de Radon. | |
| 650 | 6 | |a Théorie de la mesure. | |
| 650 | 6 | |a Cauchy, Transformée de. | |
| 650 | 7 | |a Cauchy transform |2 fast | |
| 650 | 7 | |a Measure theory |2 fast | |
| 650 | 7 | |a Radon measures |2 fast | |
| 650 | 7 | |a Transformations (Mathematics) |2 fast | |
| 710 | 2 | |a American Mathematical Society, |e publisher. | |
| 758 | |i has work: |a Rectifiable measures, square functions involving densities, and the Cauchy transform (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGyF9kjYMMdRhgtxvRGwP3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Tolsa, Xavier. |t Rectifiable measures, square functions involving densities, and the Cauchy transform. |d Providence, Rhode Island : American Mathematical Society, 2017 |w (DLC) 2016053204 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1158. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4908274 |z Texto completo |
| 880 | 8 | |6 505-01/(S |a Chapter 7. The measure and some estimates about its flatnessChapter 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 Γ^{ }; Chapter 11. The small measure of the cells from \bsb; Chapter 12. The approximating measure ^{ } on Γ^{ }ₑₓ; Chapter 13. Square function estimates for ^{ }; Chapter 14. The good measure ^{ } on Γ^{ }; Chapter 15. The ²(^{ }) norm of the density of ^{ } with respect to ^{ } | |
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| 938 | |a EBL - Ebook Library |b EBLB |n EBL4908274 | ||
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