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Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular...

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Bibliographic Details
Main Author: Pajot, Hervé M.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2002, 2002
Edition:1st ed. 2002
Series:Lecture Notes in Mathematics
Subjects:
Measure Theory
Fourier Analysis
Measure And Integration
Functions Of Complex Variables
Mathematical Analysis
Analysis
Geometry
Functions Of A Complex Variable
Analysis (mathematics)
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • Notations and conventions
  • Some geometric measures theory
  • Jones' traveling salesman theorem
  • Menger curvature
  • The Cauchy singular integral operator on Ahlfors-regular sets
  • Analytic capacity and the Painlevé Problem
  • The Denjoy and Vitushkin conjectures
  • The capacity $gamma (+)$ and the Painlevé Problem
  • Bibliography
  • Index

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