Description of interpolation spaces for the pair of local Morrey-type spaces and their generalizations
| Autor: | Burenkov, V.I., Darbayeva, D.K., Nursultanov, E.D. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | RECERCAT (Dipòsit de la Recerca de Catalunya) Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | We consider the real interpolation method and prove that for general local Morrey-type spaces, in the case when 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 non-negative non-decreasing functions on $ (0,\infty)$ . It is also shown how the classical interpolation theorems due to Stein-Weiss, Peetre, Calder\'\''{o}n, Gilbert, Lizorkin, Freitag and some of their new variants can be derived from this theorem. |
| Databáze: | OpenAIRE |
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