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

• Main Author: Tolsa, Xavier (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
• Series: Progress in Mathematics, 307
• Subjects: Mathematics.; Functions of complex variables.; Potential theory (Mathematics).; Calculus of variations.; Functions of a Complex Variable.; Potential Theory.; Calculus of Variations and Optimal Control; Optimization.

This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topi...

Table of Contents:

• Introduction
• Basic notation
• Chapter 1. Analytic capacity
• Chapter 2. Basic Calderón-Zygmund theory with non doubling measures
• Chapter 3. The Cauchy transform and Menger curvature
• Chapter 4. The capacity γ+
• Chapter 5. A Tb theorem of Nazarov, Treil and Volberg
• Chapter 6. The comparability between γ and γ +, and the semiadditivity of analytic capacity
• Chapter 7. Curvature and rectifiability
• Chapter 8. Principal values for the Cauchy transform and rectifiability
• Chapter 9. RBMO(μ) and H1 atb(μ)
• Bibliography
• Index.