Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries

We introduce a class of Morrey-type spaces , which includes the classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem for such spaces. This theorem is then applied to obtaining an analogue of O'Neil's inequality for convolutions and to proving the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operators.