Some Remarks on Spaces of Morrey Type

Abstract

We deepen the study of some Morrey type spaces, denoted by $M^{p,\lambda }\left(\Omega \right)$, defined on an unbounded open subset $\Omega$ of ${ℝ}^n$. In particular, we construct decompositions for functions belonging to two different subspaces of $M^{p,\lambda }\left(\Omega \right)$, which allow us to prove a compactness result for an operator in Sobolev spaces. We also introduce a weighted Morrey type space, settled between the above-mentioned subspaces.