Abstract and Applied Analysis
Volume 2010 (2010), Article ID 242079, 22 pages
doi:10.1155/2010/242079
Research Article

Some Remarks on Spaces of Morrey Type

Loredana Caso, Roberta D'Ambrosio, and Sara Monsurrò

Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy

Received 17 June 2010; Accepted 2 September 2010

Academic Editor: Boris Shekhtman

Copyright © 2010 Loredana Caso et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We deepen the study of some Morrey type spaces, denoted by Mp,λ(Ω), defined on an unbounded open subset Ω of ℝn. In particular, we construct decompositions for functions belonging to two different subspaces of Mp,λ(Ω), 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.