Harmonic measure and domains bounded by quasiconformal circles
HTML articles powered by AMS MathViewer
- by Donald K. Blevins
- Proc. Amer. Math. Soc. 41 (1973), 559-564
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325960-2
- PDF | Request permission
Abstract:
We index the class of quasiconformal circles by $k$ between zero and one such that $k = 0$ corresponds to arbitrary Jordan curves and $k = 1$ to circles. We establish an estimate depending on $k$ for harmonic measure in a domain bounded by a quasiconformal circle. Applications of this estimate are made to boundary correspondence under conformal maps, Hardy class of certain functions and a Phragmén-Lindelöf theorem.References
- Lars V. Ahlfors, Quasiconformal reflections, Acta Math. 109 (1963), 291–301. MR 154978, DOI 10.1007/BF02391816 A. Beurling, Etudes sur un problème de majorization, Thesis, Uppsala University, Uppsala, 1933.
- James A. Jenkins, Some uniqueness results in the theory of symmetrization, Ann. of Math. (2) 61 (1955), 106–115. MR 65640, DOI 10.2307/1969622
- Kikuji Matsumoto, On some boundary problems in the theory of conformal mappings of Jordan domains, Nagoya Math. J. 24 (1964), 129–141. MR 200430
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 559-564
- MSC: Primary 30A60; Secondary 30A78
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325960-2
- MathSciNet review: 0325960