Geodesic
Description of interpolation spaces for local Morrey-type spaces
Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 52-62

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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. 
@article{TRSPY_2010_269_a3,
     author = {V. I. Burenkov and E. D. Nursultanov},
     title = {Description of interpolation spaces for local {Morrey-type} spaces},
     journal = {Informatics and Automation},
     pages = {52--62},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a3/}
}
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V. I. Burenkov; E. D. Nursultanov. Description of interpolation spaces for local Morrey-type spaces. Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 52-62. http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a3/