On local properties of singular integral - Mamedkhanov, J. I.; Jafarov, S. Z. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.5Let $γ$ be a regular curve. We study the local properties of singular integrals in the $H_{α }^{α +β }(t_{0},γ)$ class of functions. We obtain a strengthening of the Plemelj\–Privalov theorem for functions from the class $H_{α }^{α +β}(t_{0},γ).$ It is proved that, at the point $t_{0},$ of increased smoothness for $α +β < 1,$ there is only a logarithmic loss.