Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory

1. Introduction
Xavier Tolsa

2. Basic notation
Xavier Tolsa

3. Analytic capacity
Xavier Tolsa

4. Basic Calderón-Zygmund theory with non-doubling measures
Xavier Tolsa

5. The Cauchy transform and Menger curvature
Xavier Tolsa

6. The capacity ?+
Xavier Tolsa

7. A Tb theorem of Nazarov, Treil and Volberg
Xavier Tolsa

8. The comparability between ? and ?+, and the semiadditivity of analytic capacity
Xavier Tolsa

9. Curvature and rectifiability
Xavier Tolsa

10. Principal values for the Cauchy transform and rectifiability
Xavier Tolsa

11.
RBMO (?) and




{H}_{atb}^{1}(mu)

Xavier Tolsa

Avainsanat: Mathematics, Functions of a Complex Variable, Potential Theory, Calculus of Variations and Optimal Control, Optimization