This book represents an expanded account of lectures delivered at the NSF-CBMS Regional Conference on Singular Integral Operators, held at the University of Montana in the summer of 1989. The lectures are concerned principally with developments in the subject related to the Cauchy integral on Lipschitz curves and the T(1) theorem. The emphasis is on real-variable techniques, with a discussion of analytic capacity in one complex variable included as an application.

The author has presented here a synthesized exposition of a body of results and techniques. Much of the book is introductory in character and intended to be accessible to the nonexpert, but a variety of readers should find the book useful.

Reviews

"Beautiful little book ... Numerous examples spread throughout the text show the breadth of applications which are now encompassed in this theory ... amazing the number of topics considered in a monograph of less than 130 pages."

-- Zentralblatt MATH

Table of Contents

• Examples and basic theory
• Littlewood-Paley theory
• BMO, Carleson measures and paraproducts
• The T(1) theorem
• Growth estimates
• Spaces of homogeneous type
• Analytic capacity
• Inverses of singular integral operators