On local properties of singular integral - Mamedkhanov, J. I.; Jafarov, S. Z. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.5 Let 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.