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Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
 
Xavier Tolsa ICREA, Barcelona, Spain and Universitat Autònoma de Barcelona, Spain
Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
eBook ISBN:  978-1-4704-3605-6
Product Code:  MEMO/245/1158.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
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Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
Xavier Tolsa ICREA, Barcelona, Spain and Universitat Autònoma de Barcelona, Spain
eBook ISBN:  978-1-4704-3605-6
Product Code:  MEMO/245/1158.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2452016; 130 pp
    MSC: Primary 28; 42

    Click here to view the abstract.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. A compactness argument
    • 4. The dyadic lattice of cells with small boundaries
    • 5. The Main Lemma
    • 6. The stopping cells for the proof of Main Lemma
    • 7. The measure $\tilde \mu $ and some estimates about its flatness
    • 8. The measure of the cells from ${\mathsf {BCF}}$, ${\mathsf {LD}}$, ${\mathsf {BS}\Delta }$ and ${\mathsf {BCG}}$
    • 9. The new families of cells ${{\mathsf {BS}\beta }}$, ${\mathsf {NTerm}}$, ${\mathsf {NGood}}$, ${\mathsf {NQgood}}$ and ${\mathsf {NReg}}$
    • 10. The approximating curves $\Gamma ^k$
    • 11. The small measure $\tilde \mu $ of the cells from ${{\mathsf {BS}\beta }}$
    • 12. The approximating measure $\nu ^k$ on $\Gamma ^k_{ex}$
    • 13. Square function estimates for $\nu ^k$
    • 14. The good measure $\sigma ^k$ on $\Gamma ^k$
    • 15. The $L^2(\sigma ^k)$ norm of the density of $\nu ^k$ with respect to $\sigma ^k$
    • 16. The end of the proof of the Main Lemma
    • 17. Proof of Theorem : Boundedness of $T_\mu $ implies boundedness of the Cauchy transform
    • 18. Some Calderón-Zygmund theory for $T_\mu $
    • 19. Proof of Theorem : Boundedness of the Cauchy transform implies boundedness of $T_\mu $
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2452016; 130 pp
MSC: Primary 28; 42

Click here to view the abstract.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. A compactness argument
  • 4. The dyadic lattice of cells with small boundaries
  • 5. The Main Lemma
  • 6. The stopping cells for the proof of Main Lemma
  • 7. The measure $\tilde \mu $ and some estimates about its flatness
  • 8. The measure of the cells from ${\mathsf {BCF}}$, ${\mathsf {LD}}$, ${\mathsf {BS}\Delta }$ and ${\mathsf {BCG}}$
  • 9. The new families of cells ${{\mathsf {BS}\beta }}$, ${\mathsf {NTerm}}$, ${\mathsf {NGood}}$, ${\mathsf {NQgood}}$ and ${\mathsf {NReg}}$
  • 10. The approximating curves $\Gamma ^k$
  • 11. The small measure $\tilde \mu $ of the cells from ${{\mathsf {BS}\beta }}$
  • 12. The approximating measure $\nu ^k$ on $\Gamma ^k_{ex}$
  • 13. Square function estimates for $\nu ^k$
  • 14. The good measure $\sigma ^k$ on $\Gamma ^k$
  • 15. The $L^2(\sigma ^k)$ norm of the density of $\nu ^k$ with respect to $\sigma ^k$
  • 16. The end of the proof of the Main Lemma
  • 17. Proof of Theorem : Boundedness of $T_\mu $ implies boundedness of the Cauchy transform
  • 18. Some Calderón-Zygmund theory for $T_\mu $
  • 19. Proof of Theorem : Boundedness of the Cauchy transform implies boundedness of $T_\mu $
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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