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Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
eBook ISBN:  9781470436056 
Product Code:  MEMO/245/1158.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 
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Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
eBook ISBN:  9781470436056 
Product Code:  MEMO/245/1158.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 245; 2016; 130 ppMSC: Primary 28; 42

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 CalderónZygmund theory for $T_\mu $

19. Proof of Theorem : Boundedness of the Cauchy transform implies boundedness of $T_\mu $


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Volume: 245; 2016; 130 pp
MSC: Primary 28; 42

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 CalderónZygmund theory for $T_\mu $

19. Proof of Theorem : Boundedness of the Cauchy transform implies boundedness of $T_\mu $
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