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

Abstract

We introduce a class of Morrey-type spaces M_p,q,Ω^λ, 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.