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Mat. Sb., 1989, Volume 180, Number 11, Pages 1443–1461 (Mi msb1669)  

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

Approximation of solutions of the equation $\overline\partial^jf=0$, $j\geqslant1$, in domain with quasiconformal boundary

V. V. Andrievskii, V. I. Belyi, V. V. Maimeskul


Abstract: This article establishes direct and inverse theorems of approximation theory (of the same type as theorems of Dzyadyk) that describe the quantitative connection between the smoothness properties of solutions of the equation
$$\overline\partial^jf=0,\qquad j\geqslant1,$$
and the rate of their approximation by “module” polynomials of the form
$$ P_N(z)=\sum_{n=0}^{j-1}\sum_{m=0}^{N-n}a_{m,n}z^m\overline z^n,\qquad N\geqslant j-1. $$
In particular, a constructive characterization is obtained for generalized Hölder classes of such functions on domains with quasiconformal boundary.
Bibliography: 19 titles.

Full text: PDF file (896 kB)
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English version:
Mathematics of the USSR-Sbornik, 1991, 68:2, 303–323

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10, 41A10, 30G30; Secondary 30C60
Received: 09.10.1988

Citation: V. V. Andrievskii, V. I. Belyi, V. V. Maimeskul, “Approximation of solutions of the equation $\overline\partial^jf=0$, $j\geqslant1$, in domain with quasiconformal boundary”, Mat. Sb., 180:11 (1989), 1443–1461; Math. USSR-Sb., 68:2 (1991), 303–323

Citation in format AMSBIB
\Bibitem{AndBelMai89}
\by V.~V.~Andrievskii, V.~I.~Belyi, V.~V.~Maimeskul
\paper Approximation of solutions of the equation $\overline\partial^jf=0$, $j\geqslant1$, in domain with quasiconformal boundary
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 11
\pages 1443--1461
\mathnet{http://mi.mathnet.ru/msb1669}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1034423}
\zmath{https://zbmath.org/?q=an:0704.35034|0712.35032}
\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 68
\issue 2
\pages 303--323
\crossref{https://doi.org/10.1070/SM1991v068n02ABEH002106}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991FE73700001}


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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 V. Andrievskii, “Constructive Theory of Analytic Functions on a Quasidisk”, Comput. Methods Funct. Theory, 1:1 (2002), 165  crossref  mathscinet
    2. Leonhard Frerick, Jürgen Müller, “Polynomial Approximation on Compact Sets Bounded by Dini-Smooth Arcs”, Comput. Methods Funct. Theory, 3:1 (2004), 273  crossref  mathscinet
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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