Geodesic
A discrete version of local Morrey spaces
Izvestiya. Mathematics , Tome 81 (2017) no. 1, pp. 1-28.

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We describe a new class of spaces which contains the classical Morrey spaces. Using a new approach, we prove definitive versions of duality and interpolation theorems for these spaces. The results obtained here are also of interest for the classical Morrey spaces.
Keywords: general discrete Morrey spaces, dual spaces of Morrey spaces, interpolation of Morrey spaces. 
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E. I. Berezhnoi. A discrete version of local Morrey spaces. Izvestiya. Mathematics , Tome 81 (2017) no. 1, pp. 1-28. http://geodesic.mathdoc.fr/item/IM2_2017_81_1_a0/

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