On some classes of polysingular integral equations (Q1920763)

Special singular multidimensional integral equations with perturbation arise in studying a number of problems of integral geometry. Investigation of perturbations that do not violate uniqueness of a solution is of particular interest. We study some classes of perturbed singular integral equations in the three-dimensional case. Observe that, in contrast to the planar case, the problem of solving such equations can be both strongly and weakly ill-posed. We prove uniqueness theorems and in the case of weak ill-posedness we prove an existence theorem.