ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30, 28, 42 O’Neill, Bruce, American University in Cairo Boundary Behavior of Conformal Mappings Associated with Singular Measures It is well known that the derivative of a conformal map onto a rectifiably bounded Jordan domain is in H1. It is also well known by explicit constructions (the domains not of Smirnov Type) that there may be a continuous singular measure determining the inner factor. These results are extended to the case where the domain may have inaccessible boundary points (and the prime end topology must be used). A corresponding factorisation involving singular measures, or in some cases distributions, is given.