Harmonic functions in quasicircle domains

Hinkkanen, A.

doi:10.1007/978-1-4613-9602-4_6

A. Hinkkanen⁶^nAff7

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 10))

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Abstract

Let G be a bounded plane domain whose boundary consists of finitely many disjoint quasicircles. Let u be a harmonic in G and continuous in \(\bar G\),the closure of G. We assume that the modulus of continuity of u is majorized by a suitable type of function on the boundary of G and obtain estimates for the modulus of continuity ofuin\(\bar G\).We show by examples that in a certain sense these estimates are best possible.

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References

Ahlfors, L.V., QuasiconformaJ reflections, Acta Math. 109 (1963), 291–301.
Article MATH MathSciNet Google Scholar
Blevins, D.K., Some properties of domains bounded by quasiconformal circles, University of Michigan Ph.D.-thesis, 1972.
Google Scholar
Blevins, D.K., Harmonic measure and domains bounded by quasiconformal circles, Proc. Amer. Math. Soc. 41 (1973), 559–564.
Article MATH MathSciNet Google Scholar
Gehring, F.W. and Martio, O., Quasidisks and the Hardy-Littlewood property. Complex Variables 2 (1983), 67–78.
MATH MathSciNet Google Scholar
Hayman, W.K. and Weitsman, A., On the coefficients and means of functions omitting values, Math. Proc. Cambridge Phil. Soc. 77 (1975), 119–137.
Article MATH MathSciNet Google Scholar
Hinkkanen, A., Modulus of continuity of harmonic functions, to appear.
Google Scholar
Tsuji, M., Potential theory in modern function theory, Maruzen, Tokyo, 1959.
MATH Google Scholar
Zinsmeister, M., Problèmes de Dirichlet, Neumann, Calderón dans les quasidisques pour les classes Hölderiennes, to appear.
Google Scholar

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A. Hinkkanen
Present address: Dept. of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109-1003, USA

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Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California, 94720, USA
A. Hinkkanen

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A. Hinkkanen
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Editors and Affiliations

Department of Mathematics, Purdue University, West Layfayete, IN, 47909, USA
D. Drasin
Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA
I. Kra
Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA
C. J. Earle
Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA
A. Marden
Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA
F. W. Gehring

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Hinkkanen, A. (1988). Harmonic functions in quasicircle domains. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_6

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DOI: https://doi.org/10.1007/978-1-4613-9602-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9604-8
Online ISBN: 978-1-4613-9602-4
eBook Packages: Springer Book Archive

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