Description of interpolation spaces for local Morrey-type spaces

V. I. Burenkov ; E. D. Nursultanov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 52-62.

Résumé

We consider the real interpolation method and prove that for local Morrey spaces, in the case when they have the same integrability parameter, the interpolation spaces are again local Morrey-type spaces with appropriately chosen parameters. Thus, in contrast to the standard Morrey-type spaces, these local spaces form an interpolation scale. In particular, this is true in the so-called nondiagonal case.

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