On boundedness of the generalized Riesz potential in local Morrey type spaces.

Well-known results on the boundedness of the classical Riesz potential in local Morrey-type spaces are generalized to the case of integral operators of Riesz type, in which the power function is replaced by a general function that satisfies certain conditions. For some values of numerical parameters characterizing local Morrey-type spaces, necessary and sufficient conditions on functional parameters are obtained that ensure the boundedness of such operators from one general local Morrey-type space to another.