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Title: Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces
Author: Almeida, Alexandre
Samko, Stefan
Keywords: Local Morrey space
Global Morrey space
Generalized Morrey space
Weighted Lebesgue space
Stummel space
Stummel classes
Issue Date: 2017
Publisher: Elsevier
Abstract: We prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces). In particular, we obtain embeddings into a new Stummel class of functions with some vanishing property at infinity. We also partially improve a known result on the coincidence of Stummel spaces with a modification of Morrey spaces where the supremum norm is replaced by an integral Lp-norm.
Peer review: yes
DOI: 10.1016/
ISSN: 0362-546X
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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