Abstract:
For the case of a bounded Jordan domain $G\subset\mathbf C$ with quasiconformal boundary, the author solves the problem, posed by V. K. Dzyadyk in the mid-sixties, of a constructive description of the classes of functions that are harmonic in $G$ and continuous on $\overline G$, with given majorant of their modulus of continuity.
Some assertions reflecting the close connection between the geometric structure of $G$ and contour-solid properties of harmonic functions in $G$ are proved.
Bibliography: 23 titles.
Citation:
V. V. Andrievskii, “A constructive characterization of harmonic functions in domains with quasiconformal boundaries”, Math. USSR-Izv., 34:2 (1990), 441–454
\Bibitem{And89}
\by V.~V.~Andrievskii
\paper A~constructive characterization of harmonic functions in domains with quasiconformal boundaries
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 441--454
\mathnet{http://mi.mathnet.ru/eng/im1249}
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000661}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=998305}
\zmath{https://zbmath.org/?q=an:0732.31002}
Linking options:
https://www.mathnet.ru/eng/im1249
https://doi.org/10.1070/IM1990v034n02ABEH000661
https://www.mathnet.ru/eng/im/v53/i2/p425
This publication is cited in the following 6 articles:
Vladimir V. Andrievskii, Stephan Ruscheweyh, “Remez-Type Inequalities in Terms of Linear Measure”, Comput. Methods Funct. Theory, 5:2 (2006), 347
Vladimir V. Andrievskii, Hans-Peter Blatt, Springer Monographs in Mathematics, Discrepancy of Signed Measures and Polynomial Approximation, 2002, 1
V.V. Andrievskii, Handbook of Complex Analysis, 1, Geometric Function Theory, 2002, 493
T. J. Rivlin, Joseph L. Walsh, 2000, 457
Vladimir Andrievskii, Hans-Peter Blatt, “Erdős–Turán Type Theorems on Quasiconformal Curves and Arcs”, Journal of Approximation Theory, 97:2 (1999), 334
Vladimir Andrievskii, “Approximation of analytic functions and their real part”, Constr. Approx, 8:2 (1992), 233
Citation in format AMSBIB
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