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 Calderon 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.

Springer Book Archives

Book Information
ISBN 9783540190912
Author Takafumi Murai
Format Paperback
Page Count 134
Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG