A Balakrishnan-Rubin type hypersingular integral operator and inversion of Flett potentials

Abstract

In the present paper we introduce new ``truncated" hypersingular integral operators $D_{\epsilon}^{\alpha}f,(\epsilon>0)$ generated by the modified Poisson semigroup and obtain an explicit inversion formula for the Flett potentials in framework of $L_p$--spaces.********************************************************************************************************************************************************************************************************************************************************************************************************