Complex interpolation and Calderón–Mityagin couples of Morrey spaces

Abstract

We study interpolation spaces between global Morrey spaces and between local Morrey spaces. We prove that for a wide class of couples of these spaces the upper complex Calderon spaces are not described by the K-method of interpolation. A by-product of our results is that couples of Morrey spaces belonging to this class are not Calderon–Mityagin couples. A Banach couple (X0,X1) is said to have the universal K-property if all relative interpolation spaces from any Banach couple to (X0,X1) are relatively K-monotone. A couple of local Morrey spaces is proved to have the universal K-property once it is a Calderon–Mityagin couple.