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We deepen the study of some Morrey typespaces, denoted by Mp,λ(Ω), defined on an unbounded open subset Ω of ℝn. In particular, we construct decompositions for functions belonging to two differentsubspaces of Mp,λ(Ω), which allow us to prove a compactness result for anoperator in Sobolev spaces. We also introduce a weighted Morrey type space,settled between the above-mentioned subspaces

Some Remarks on Spaces of Morrey Type