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

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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Tolsa, Xavier (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
Edition:1st ed. 2014.
Series:Progress in Mathematics, 307
Subjects:
Functions of complex variables.
Potential theory (Mathematics).
Mathematical optimization.
Calculus of variations.
Functions of a Complex Variable.
Potential Theory.
Calculus of Variations and Optimization.
Online Access:Texto Completo
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.

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