On approximation of hypersingular integral operators by bounded ones

We solve the Stechkin problem about approximation of generally speaking unbounded hypersingular integral operators by bounded ones. As a part proof, we also several related and interesting on their own problems. In particular, obtain sharp Landau-Kolmogorov type inequalities in both additive multiplicative forms for prove Ostrowski inequality multivatiate Sobolev classes. give some applications obtained results, particular study modulus continuity operators, optimal recovery value operator based argument known with an error.