#### Vol. 12, No. 7, 2019

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Complex interpolation and Calderón–Mityagin couples of Morrey spaces

### Mieczysław Mastyło and Yoshihiro Sawano

Vol. 12 (2019), No. 7, 1711–1740
##### 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 Calderón 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 Calderón–Mityagin couples. A Banach couple $\left({X}_{0},{X}_{1}\right)$ is said to have the universal $K$-property if all relative interpolation spaces from any Banach couple to $\left({X}_{0},{X}_{1}\right)$ are relatively $K$-monotone. A couple of local Morrey spaces is proved to have the universal $K$-property once it is a Calderón–Mityagin couple.

##### Keywords
interpolation spaces, complex method, $K$-method, Morrey spaces
##### Mathematical Subject Classification 2010
Primary: 46B70
Secondary: 42A45, 42B30
##### Milestones
Received: 12 October 2017
Revised: 3 September 2018
Accepted: 19 December 2018
Published: 22 July 2019
##### Authors
 Mieczysław Mastyło Faculty of Mathematics and Computer Science Adam Mickiewicz University Poznań Poland Yoshihiro Sawano Department of Mathematics and Information Sciences Tokyo Metropolitan University Tokyo Japan