On local properties of singular integral

Abstract

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.