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

The notion of a μ -smooth point of a L p -function φ and a family of truncated hypersingular integrals depending on a parameter ε are introduced. Then the connection between the order of μ -smoothness of the function φ and the rate of convergence of the family of truncated hypersingular integrals to φ , when ε tends to 0, is obtained.