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Mat. Sb., 1992, Volume 183, Number 2, Pages 21–37 (Mi msb1471)  

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

The Plemelj–Privalov theorem for generalized Hölder classes

E. G. Guseinov


Abstract: The Plemelj–Privalov theorem on invariance of the Hölder classes $H_\alpha$, $0<\alpha<1$, with respect to a one-dimensional singular integral with Cauchy kernel on closed smooth Jordan curves is well known. V. V. Salaev posed the problem of describing the class $\Pi_\alpha$ of all closed rectifiable Jordan curves on which the Plemelj–Privalov theorem is valid; it was solved in a paper by Salaev, Guseinov, and Seifullaev, where a condition completely characterizing the class $ \Pi_\alpha$ is given in terms of the planar measure of boundary strips of sets constructed from the curve. The present article is devoted to the solution of Salaev's problem for the generalized Hölder class $H_\varphi$.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 165–182

Bibliographic databases:

MSC: Primary 30C40; Secondary 42B20, 26A26
Received: 05.02.1990

Citation: E. G. Guseinov, “The Plemelj–Privalov theorem for generalized Hölder classes”, Mat. Sb., 183:2 (1992), 21–37; Russian Acad. Sci. Sb. Math., 75:1 (1993), 165–182

Citation in format AMSBIB
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\paper The Plemelj--Privalov theorem for generalized H\"older classes
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 2
\pages 21--37
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..75..165G}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 165--182
\crossref{https://doi.org/10.1070/SM1993v075n01ABEH003378}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Igor Pritsker, “How to Find a Measure from its Potential”, Comput. Methods Funct. Theory, 8:2 (2008), 597  crossref
    2. Jaroslav Drobek, “On estimate for the modulus of continuity of the Cauchy-type integral having a Lipschitz-continuous density”, Math. Slovaca, 63:1 (2013), 83  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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