On behaviour of the family of weak singular integral operators with respect to degree of singularity

In the present thesis, the family of integral operators (so-called beta-semigroup) generalizing classical Gauss-Weierstrass and Abel-Poisson semigroups are introduced. By making use of this beta-semigroup, a two-parameter family of integral operators is defined. These integral operators generalize the classical Bessel and Flett potentials. We investigate the approximation properties of this family of integral operators when one of the parameters tends to zero. We show that the order of approximation at the Lipschitz points of the function does not depend on the Lipschitz degree.