02945cam  2200409 i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000340013305000220016708200160018910000190020524501300022426400700035430000530042433600260047733700280050333800270053149000740055850000660063250400570069850511940075550600500194953300950199953800360209458800470213065000200217765000200219765000220221765000340223977601700227385600440244385600480248719379090RPAM20170613150046.0ma     b    000 0 cr/|||||||||||170613s2017    riua    ob    000 0 eng    a9781470436056 (online)  aDLCbengcDLCerdadDLCdRPAM00aQA312b.T635 201700a515/.422231 aTolsa, Xavier.10aRectifiable measures, square functions involving densities, and the cauchy transform /h[electronic resource] cXavier Tolsa. 1aProvidence, Rhode Island :bAmerican Mathematical Society,c2017.  a1 online resource (v, 130 pages : illustrations)  atextbtxt2rdacontent  aunmediatedbn2rdamedia  avolumebnc2rdacarrier0 aMemoirs of the American Mathematical Society, x1947-6221 ; vv. 1158  a"Volume 245, number 1158 (third of 6 numbers), January 2017."  aIncludes bibliographical references (pages 129-130).00tChapter 1. IntroductiontChapter 2. PreliminariestChapter 3. A compactness argumenttChapter 4. The dyadic lattice of cells with small boundariestChapter 5. The Main LemmatChapter 6. The stopping cells for the proofof Main Lemma 5.1tChapter 7. The measure $\tilde \mu $ and some estimatesabout its flatnesstChapter 8. The measure of the cells from $\BCF $, $\LD $, $\BSD $and $\BCG $tChapter 9. The new families of cells $\bsb $, $\nterm $, $\ngood $, $\nqgood $ and $\nreg $tChapter 10. The approximating curves $\Gamma ^k$tChapter 11. The small measure $\tilde \mu $ of the cells from $\bsb $tChapter 12. The approximating measure $\nu ^k$ on $\Gamma ^k_ex$tChapter 13. Square function estimates for $\nu ^k$tChapter 14. The good measure $\sigma ^k$ on $\Gamma ^k$tChapter 15. The $L^2(\sigma ^k)$ norm of the density of $\nu ^k$ with respect to $\sigma ^k$tChapter 16. The end of the proof of the Main Lemma 5.1tChapter 17. Proof of Theorem 1.3: Boundedness of $T_\mu $ implies boundedness of the Cauchy transformtChapter 18. Some Calderâon-Zygmund theory for $T_\mu $tChapter 19. Proof of Theorem 1.3: Boundedness of the Cauchy transform implies boundedness of $T_\mu $1 aAccess is restricted to licensed institutions  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2017  aMode of access : World Wide Web  aDescription based on print version record. 0aRadon measures. 0aMeasure theory. 0aCauchy transform. 0aTransformations (Mathematics)0 iPrint version: aTolsa, Xavier.tRectifiable measures, square functions involving densities, and the cauchy transform /w(DLC)   2016053204x0065-9266z97814704225234 3Contentsuhttp://www.ams.org/memo/1158/4 3Contentsuhttps://doi.org/10.1090/memo/1158