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

  • Book
  • © 1988

Overview

Authors:
  1. Takafumi Murai
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1307)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-VII
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  2. The calderón commutator (8 proofs of its boundedness)

    • Takafumi Murai
    Pages 1-30

  3. A real variable method for the cauchy transform on graphs

    • Takafumi Murai
    Pages 31-70

  4. Analytic capacities of cranks

    • Takafumi Murai
    Pages 71-116

  5. Back Matter

    Pages 117-133
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Keywords

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.

Bibliographic Information

  • Book Title: A Real Variable Method for the Cauchy Transform, and Analytic Capacity

  • Authors: Takafumi Murai

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078078

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19091-2Published: 27 April 1988

  • eBook ISBN: 978-3-540-39105-0Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 134

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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