Method of approximating inverse operators and its applications to the inversion of potential-type integral transforms

In this survey we present some results on the inversion of potential-type integral transforms based on the method of approximating inverse operators. This method is applied to the problem of inverting potential-type integral transforms with densities in L-p-spaces and to the characterization of the function spaces of fractional smoothness, connected with the degenerated differential operators. A previous survey [21] was devoted to the method of hypersingular integrals in application to inversion problems.*.