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 (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 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