On a rate of convergence of truncated hypersingular integrals associated to Riesz and Bessel potentials

The notion of a μμ-smooth point of a LpLp-function φφ and a family of truncated hypersingular integrals depending on a parameter εε are introduced. Then the connection between the order of μμ-smoothness of the function φφ and the rate of convergence of the family of truncated hypersingular integrals to φφ, when εε tends to 0, is obtained.