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- On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operatorsPublication . Alabalik, Aysegul C.; Almeida, Alexandre; Samko, StefanWe consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of C-0(infinity) (R-n) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy-Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.
- Approximation in Morrey spacesPublication . Almeida, Alexandre; Samko, StefanA new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions is introduced. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalisation of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained. (C) 2016 Elsevier Inc. All rights reserved.
- Preservation of certain vanishing properties of generalized Morrey spaces by some classical operatorsPublication . Alabalik, Aysegul C.; Almeida, Alexandre; Samko, StefanWe show that certain vanishing properties defining closed subspaces of generalized Morrey spaces are preserved under the action of various classical operators of harmonic analysis, such as maximal operators, singular-type operators, Hardy operators, and fractional integral operators. Those vanishing subspaces were recently used to deal with the delicate problem on the description of the closure of nice functions in Morrey norm.
- Embeddings of variable Hajlasz-Sobolev spaces into holder spaces of variable orderPublication . Almeida, Alexandre; Samko, StefanPointwise estimates in variable exponent Sobolev spaces on quasi-metric measure spaces are investigated. Based on such estimates, Sobolev embeddings into Holder spaces with variable order are obtained. This extends some known results to the variable exponent setting. (C) 2008 Elsevier Inc. All rights reserved.
- Embeddings of local generalized Morrey spaces between weighted Lebesgue spacesPublication . Almeida, Alexandre; Samko, StefanWe 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 L-p-norm. (C) 2017 Elsevier Ltd. All rights reserved.