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Matematicheskie Zametki, 1976, Volume 19, Issue 3, Pages 365–380 (Mi mzm7755)  

This article is cited in 19 scientific papers (total in 19 papers)

Direct and inverse estimates for a singular Cauchy integral along a closed curve

V. V. Salaev

Azerbaidzhan State University
Abstract: A new metric characteristic $\theta(\delta)$ of rectifiable Jordan curves is introduced. We will find an estimate of the type of the Zygmund estimate for an arbitrary rectifiable closed Jordan curve in its terms. It is shown that the Plemel'–Privalov theorem on the invariance of Holder's spaces is true for the class of curves satisfying the condition $\theta(\delta)\sim\delta$, which is much wider than the class of piecewise smooth curves (the presence of cusps is admissible). The Bari–Stechkin theorem on the necessary conditions of action of a singular operator in the spaces $H_\omega$ is generalized. It is shown that this theorem is valid for every curve which has a continuous tangent at least at one point and $\theta(\delta)\sim\delta$.
Received: 26.03.1975
English version:
Mathematical Notes, 1976, Volume 19, Issue 3, Pages 221–231
DOI: https://doi.org/10.1007/BF01437855
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: V. V. Salaev, “Direct and inverse estimates for a singular Cauchy integral along a closed curve”, Mat. Zametki, 19:3 (1976), 365–380; Math. Notes, 19:3 (1976), 221–231
Citation in format AMSBIB
\Bibitem{Sal76}
\by V.~V.~Salaev
\paper Direct and inverse estimates for a singular Cauchy integral along a~closed curve
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 3
\pages 365--380
\mathnet{http://mi.mathnet.ru/mzm7755}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=410234}
\zmath{https://zbmath.org/?q=an:0351.44006|0345.44006}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 3
\pages 221--231
\crossref{https://doi.org/10.1007/BF01437855}
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  • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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