
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 onedimensional 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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Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 165–182
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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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\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 165182
\crossref{https://doi.org/10.1070/SM1993v075n01ABEH003378}
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