Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations

Burenkov, Victor, Nursultanov, E. and Chigambayeva, D. K. 2014. Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations. Proceedings of the Steklov Institute of Mathematics 284 (1) , pp. 97-128. 10.1134/S0081543814010064

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Abstract

The real interpolation method is considered and it is proved that for general local Morrey-type spaces, in the case in which they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters. This result is a particular case of the interpolation theorem for much more general spaces defined with the help of an operator acting from some function space to the cone of nonnegative nondecreasing functions on (0, ∞). It is also shown how the classical interpolation theorems due to Stein-Weiss, Peetre, Calderón, Gilbert, Lizorkin, Freitag and some of their new variants can be derived from this theorem.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0081-5438
Last Modified:	04 Jun 2017 08:47
URI:	https://orca.cardiff.ac.uk/id/eprint/84894

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