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

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