Investigation of the rate of convergence of truncated hypersingular integral families generated by various semigroups

In Harmonic Analysis, an important problem is to obtain inversion formulas for the potential-type integral operators. The studies on this subject have been developed by the use of hypersingular integral techniques. In this thesis, the families of truncated hypersingular integrals generated by the Poisson, metaharmonic and Gauss-Weierstrass semigroups and dependent on a parameter ε, are introduced. Then the connection between the order of smoothness of a given L_{p}-function ϕ and the rate of convergence of these families of truncated hypersingular integrals, which converge to ϕ when ε tends to 0, is obtained. Also, similar problem is expressed for generalized Riesz potentials in framework of Fourier-Bessel Harmonic Analysis.