Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces

• Autor(a) principal: Almeida, Alexandre
• Data de Publicação: 2017
• Outros Autores: Samko, Stefan
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/18638
• topic: Local Morrey space; Global Morrey space; Generalized Morrey space; Weighted Lebesgue space; Embeddings; Stummel space; Stummel classes

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.