Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces

We introduce a class of Morrey-type spaces $M_{p,q,\Omega}^\lambda$, which includes the classical Morrey spaces. We discuss their properties and we prove a Marcinkiewicz-type interpolation theorem. This theorem is then applied to obtaining a Young–O'Neil-type inequality for the convolution operator in Morrey-type spaces.