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On Local Properties of Singular Integrals

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Ukrainian Mathematical Journal Aims and scope

Let γ be a regular curve. We study the local properties of singular integrals in the class of functions \({H}_{\alpha }^{\alpha +\beta }\left({t}_{0},\upgamma \right).\) We obtain a strengthening of the Plemelj–Privalov theorem for functions from the class \({H}_{\alpha }^{\alpha +\beta }\left({t}_{0},\upgamma \right).\) It is proved that, at the point t0 of increased smoothness for α+β < 1, there is only a logarithmic loss.

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Authors and Affiliations

  1. Baku State University, Baku, Azerbaijan

    J. I. Mamedkhanov

  2. Muş Alparslan University, Muş, Turkey

    S. Z. Jafarov

  3. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    S. Z. Jafarov

Authors
  1. J. I. Mamedkhanov
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  2. S. Z. Jafarov
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Correspondence to J. I. Mamedkhanov.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 614–627, May, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i5.6959.

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Mamedkhanov, J.I., Jafarov, S.Z. On Local Properties of Singular Integrals. Ukr Math J 75, 703–718 (2023). https://doi.org/10.1007/s11253-023-02224-4

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  • DOI: https://doi.org/10.1007/s11253-023-02224-4

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