The Rate of Convergence of Truncated Hypersingular Integrals Generated by the Generalized Poisson Semigroup

Abstract

We introduce a family of Balakrishnan-Rubin type hypersingular integrals depending on a parameter $\varepsilon $ and generated by the Generalized Poisson semigroup. Then the rate of convergence of these families of truncated hypersingular integrals, which converge to $L_{p,\nu }$--function $\varphi $ as $\varepsilon $ tends to $0$, is obtained.

Keywords

• flett potentials
• truncated hypersingular integrals
• rate of convergence
• generalized poisson semigroup