Author	Murai, Takafumi. author
Title	A Real Variable Method for the Cauchy Transform, and Analytic Capacity [electronic resource] / by Takafumi Murai
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1988
Connect to	http://dx.doi.org/10.1007/BFb0078078
Descript	X, 134 p. online resource

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 Calderรณn 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

The calderรณn commutator (8 proofs of its boundedness) -- A real variable method for the cauchy transform on graphs -- Analytic capacities of cranks

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Physics
5. Mathematics
6. Analysis
7. Theoretical
8. Mathematical and Computational Physics