TY  - BOOK
AU  - Murai,Takafumi
TI  - A real variable method for the Cauchy transform and analytic capacity
T2  - Lecture notes in mathematics,
SN  - 9783540391050
AV  - QA3QA360 .L28 no. 1307
U1  - 510 s515 19
PY  - 1988///
CY  - Berlin, New York
PB  - Springer-Verlag
KW  - Geometric function theory
KW  - Cauchy transform
KW  - Analytic functions
KW  - Functional analysis
KW  - Transformations (Mathematics)
KW  - Cauchy problem
KW  - Analyse fonctionnelle
KW  - Transformations (Mathématiques)
KW  - Problème de Cauchy
KW  - Théorie géométrique des fonctions
KW  - Cauchy, Transformée de
KW  - Fonctions analytiques
KW  - Funciones analíticas
KW  - embne
KW  - Análisis funcional
KW  - Transformaciones (Matemáticas)
KW  - Funciones, Teoría geométrica de
KW  - embucm
KW  - fast
KW  - Analytische Kapazität
KW  - gnd
KW  - Cauchy-Transformierte
KW  - Cauchy, Transformació de
KW  - lemac
KW  - Nombres reals
KW  - Anàlisi funcional
KW  - Geometria algebraica
KW  - nli
N1  - Includes bibliographical references (pages 129-131) and index; The Caldern Commutator (8 Proofs of its Boundedness) -- A Real Variable Method for the Cauchy Transform on Graphs -- Analytic Capacities of Cranks -- Appendix I -- Appendix II -- References -- Subject Index; Electronic reproduction; [Place of publication not identified]; HathiTrust Digital Library; 2010
N2  - 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 Caldern 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
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/BFb0078078
ER  -