A Real Variable Method for the Cauchy Transform, and Analytic Capacity

  • Authors
  • Takafumi Murai

Part of the Lecture Notes in Mathematics book series (LNM, volume 1307)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Takafumi Murai
    Pages 71-116
  3. Back Matter
    Pages 117-133

About this book


This research monograph studies the Cauchy transform on curves with the object of formulating a precise estimate of analytic capacity. The note is divided into three chapters. The first chapter is a review of the Calderón commutator. In the second chapter, a real variable method for the Cauchy transform is given using only the rising sun lemma. The final and principal chapter uses the method of the second chapter to compare analytic capacity with integral-geometric quantities. The prerequisites for reading this book are basic knowledge of singular integrals and function theory. It addresses specialists and graduate students in function theory and in fluid dynamics.


DEX Lemma Singular integral dynamics form function graphs integral knowledge object proof review variable

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19091-2
  • Online ISBN 978-3-540-39105-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site