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

The 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 power function is replaced by a general function satisfying certain conditions. For some values of the numerical parameters characterizing local Morrey type spaces necessary and sufficient conditions on the functional parameters are obtained ensuring the boundedness of such operators from one general local Morrey-type space to another one.