Abstract
The goal of this article is to study the Dirichlet problem for holomorphic functions in the unit disk in scales of spaces of modulus of continuity. Using scales, we are able to describe the loss of regularity of the solution in comparison with the given Dirichlet data. Some examples for data which are close to continuous data or close to Lipschitz data complete this article.
Acknowledgements
Part of the results are obtained during the stay of A.S. Ilschukov as Euler-fellow at the Faculty of Mathematics and Computer Science of Technical University Bergakademie Freiberg in February/March 2010. All authors thank DAAD for their financial support.
Notes
†Doz. Dr. A. Timofeev passed away on August 19 2011 near Ufa. He has been buried in Syktyvkar.