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

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 particul...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2014, Vol.284 (1), p.97-128
Main Authors: Burenkov, V. I., Nursultanov, E. D., Chigambayeva, D. K.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543814010064