Translator Disclaimer
2019 Complex interpolation and Calderón–Mityagin couples of Morrey spaces
Mieczysław Mastyło, Yoshihiro Sawano
Anal. PDE 12(7): 1711-1740 (2019). DOI: 10.2140/apde.2019.12.1711

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.

Citation

Download Citation

Mieczysław Mastyło. Yoshihiro Sawano. "Complex interpolation and Calderón–Mityagin couples of Morrey spaces." Anal. PDE 12 (7) 1711 - 1740, 2019. https://doi.org/10.2140/apde.2019.12.1711

Information

Received: 12 October 2017; Revised: 3 September 2018; Accepted: 19 December 2018; Published: 2019
First available in Project Euclid: 31 July 2019

zbMATH: 07115632
MathSciNet: MR3986539
Digital Object Identifier: 10.2140/apde.2019.12.1711

Subjects:
Primary: 46B70
Secondary: 42A45, 42B30

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 7 • 2019
MSP
Back to Top