On Local Properties of Singular Integrals

Abstract

Let-gamma be a regular curve. We study the local properties of singular integrals in the class of functions H-alpha(alpha+beta) (t(0), gamma). 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 t0 of increased smoothness for alpha + beta < 1, there is only a logarithmic loss.