2018
DOI: 10.1515/gmj-2018-0023
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Approximation in generalized Morrey spaces

Abstract: In this paper we study the approximation of functions from generalized Morrey spaces by nice functions. We introduce a new subspace whose elements can be approximated by infinitely differentiable compactly supported functions. This provides, in particular, an explicit description of the closure of the set of such functions in generalized Morrey spaces.

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Cited by 12 publications
(11 citation statements)
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“…. We refer to Almeida and Samko 27 for further details and also strictness embedding results and concrete examples of Morrey functions living is such subspaces. Note also that complex interpolation of such vanishing subspaces was recently studied in Hakim and Sawano 47 (see also Yuan et al 48 for related results) in the classical case (ie, with the choice (t) = t ).…”
Section: Generalized Morrey Spaces and Vanishing Subspacesmentioning
confidence: 99%
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“…. We refer to Almeida and Samko 27 for further details and also strictness embedding results and concrete examples of Morrey functions living is such subspaces. Note also that complex interpolation of such vanishing subspaces was recently studied in Hakim and Sawano 47 (see also Yuan et al 48 for related results) in the classical case (ie, with the choice (t) = t ).…”
Section: Generalized Morrey Spaces and Vanishing Subspacesmentioning
confidence: 99%
“…As regards the generalized counterpart at infinity, V ∞ L p, (R n ), and the subspace V ( * ) L p, (R n ), they were first considered in Almeida and Samko. 27 It turns out that the subspace V ( * ) 0,∞ L p, (R n ), collecting all those Morrey functions with the three vanishing properties (V 0 ), (V ∞ ), and (V * ), provides an explicit description of the closure of C ∞ 0 (R n ) in generalized Morrey spaces L p, (R n ), see Almeida and Samko. 27 The operators of harmonic analysis we shall deal with, such as maximal operators, singular operators, potential operators, and Hardy operators, are known to be bounded in the spaces L p, (R n ) under appropriate assumptions on the parameters p and , see, eg, the papers.…”
Section: Introductionmentioning
confidence: 99%
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