On the rate of Lp -convergence of Balakrishnan Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup

Abstract

We introduce a family of Balakrishnan Rubin-type hypersingular integrals depending on a parameter ε and generated by the Gauss Weierstrass semigroup. Then the connection between the order of Lp smoothness of a Lp function φ and the rate of Lp -convergence of these families to φ, as ε tends to 0, is obtained.