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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 425–438 (Mi izv1249)  

This article is cited in 2 scientific papers (total in 2 papers)

A constructive characterization of harmonic functions in domains with quasiconformal boundaries

V. V. Andrievskii


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.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 441–454

Bibliographic databases:

UDC: 517.5
MSC: Primary 31A25, 30C85; Secondary 30C75
Received: 06.04.1987

Citation: V. V. Andrievskii, “A constructive characterization of harmonic functions in domains with quasiconformal boundaries”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 425–438; Math. USSR-Izv., 34:2 (1990), 441–454

Citation in format AMSBIB
\Bibitem{And89}
\by V.~V.~Andrievskii
\paper A~constructive characterization of harmonic functions in domains with quasiconformal boundaries
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 425--438
\mathnet{http://mi.mathnet.ru/izv1249}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998305}
\zmath{https://zbmath.org/?q=an:0732.31002}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 441--454
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000661}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vladimir Andrievskii, Hans-Peter Blatt, “Erdős–Turán Type Theorems on Quasiconformal Curves and Arcs”, Journal of Approximation Theory, 97:2 (1999), 334  crossref
    2. Vladimir V. Andrievskii, Stephan Ruscheweyh, “Remez-Type Inequalities in Terms of Linear Measure”, Comput. Methods Funct. Theory, 5:2 (2006), 347  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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