Harmonic measure and domains bounded by quasiconformal circles
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- by Donald K. Blevins PDF
- Proc. Amer. Math. Soc. 41 (1973), 559-564 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
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- Kikuji Matsumoto, On some boundary problems in the theory of conformal mappings of Jordan domains, Nagoya Math. J. 24 (1964), 129–141. MR 200430
Additional 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