The Calderón construction for a couple of global Morrey spaces

We employ a new approach to show that the Calderón construction for a couple of global Morrey spaces coincides with the Morrey space with appropriate parameters only under rather strong assumptions on the couples of ideal spaces that parameterize the original Morrey spaces. We show that, in the case of classical examples of global Morrey spaces, these assumptions are necessary and sufficient. Applying a well-known reduction, we use the Calderón construction for a couple of global Morrey spaces to describe the spaces given by the complex interpolation method and also to prove new interpolation theorems for global Morrey spaces.