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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1309–1321 (Mi izv1342)  

This article is cited in 5 scientific papers (total in 5 papers)

Mapping of sets of finite $\alpha$-measure by rational functions

E. P. Dolzhenko, V. I. Danchenko


Abstract: Inequalities are obtained which reflect the changes in the Hausdorff $\alpha$-measures, including lengths and areas, of planar sets when they are mapped by rational functions of a complex variable. Some applications of these inequalities to the theory of rational approximation are given.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 621–633

Bibliographic databases:

UDC: 517.53
MSC: Primary 30C99, 30E10, 41A20; Secondary 11K55
Received: 22.01.1986

Citation: E. P. Dolzhenko, V. I. Danchenko, “Mapping of sets of finite $\alpha$-measure by rational functions”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1309–1321; Math. USSR-Izv., 31:3 (1988), 621–633

Citation in format AMSBIB
\Bibitem{DolDan87}
\by E.~P.~Dolzhenko, V.~I.~Danchenko
\paper Mapping of sets of finite $\alpha$-measure by rational functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 6
\pages 1309--1321
\mathnet{http://mi.mathnet.ru/izv1342}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=933966}
\zmath{https://zbmath.org/?q=an:0677.30008|0673.30004}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 3
\pages 621--633
\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001093}


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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. V. I. Danchenko, “Several integral estimates of the derivatives of rational functions on sets of finite density”, Sb. Math., 187:10 (1996), 1443–1463  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Russian Math. (Iz. VUZ), 42:5 (1998), 1–3  mathnet  mathscinet  elib
    3. A. A. Pekarskii, “Bernstein type inequalities for arbitrary rational functions in the spaces $L_p$, $0<p<1$, on Lavrent'ev curves”, St. Petersburg Math. J., 16:3 (2005), 541–560  mathnet  crossref  mathscinet  zmath
    4. Dzh. I. Mamedkhanov, “O neravenstvakh raznykh metrik tipa S. M. Nikolskogo”, Tr. IMM UrO RAN, 18, no. 4, 2012, 240–248  mathnet  elib
    5. St. Petersburg Math. J., 25:3 (2014), 361–396  mathnet  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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