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Complex interpolation
and Calderón–Mityagin couples of Morrey spaces
Mieczysław Mastyło and Yoshihiro Sawano |
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Vol. 12 (2019), No. 7, 1711–1740
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Abstract |
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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 -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 is said to have the universal -property if all relative interpolation spaces from any Banach couple to are relatively -monotone. A couple of local Morrey spaces is proved to have the universal -property once it is a Calderón–Mityagin couple. |
Keywords
interpolation spaces, complex method, $K$-method, Morrey
spaces
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Mathematical Subject Classification 2010
Primary: 46B70
Secondary: 42A45, 42B30
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Milestones
Received: 12 October 2017
Revised: 3 September 2018
Accepted: 19 December 2018
Published: 22 July 2019
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Authors |
| Mieczysław Mastyło | |
| Faculty of Mathematics and Computer
Science Adam Mickiewicz University Poznań Poland |
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| Yoshihiro Sawano | |
| Department of Mathematics and
Information Sciences Tokyo Metropolitan University Tokyo Japan |
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