On local properties of singular integral

  • J. I. Mamedkhanov Baku State University, Azerbaijan
  • S. Z. Jafarov Muş Alparslan University, Turkey and Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku
Keywords: Regular curve, singular integral, H\H, local class of functios, Plemelj-Privalov theorem


UDC 517.5

Let $\gamma$ be a regular curve. We study the local properties of singular integrals in the $H_{\alpha }^{\alpha +\beta }(t_{0},\gamma)$ class of functions. We obtain a strengthening of the Plemelj\–Privalov theorem for functions from the class $H_{\alpha }^{\alpha +\beta}(t_{0},\gamma).$ It is proved that, at the point $t_{0},$ of increased smoothness for $\alpha +\beta < 1,$ there is only a logarithmic loss.


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How to Cite
MamedkhanovJ. I., and JafarovS. Z. “On Local Properties of Singular Integral”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 5, May 2023, pp. 614 -27, doi:10.37863/umzh.v75i5.6959.
Research articles