TY  - Type of reference 
TI  - Caractérisation de sous-espaces vectoriels fermés des espaces de Morrey et approximation 
AU  - Nouffou Diarra 
AU  - Ibrahim Fofana 
AB  - Let $$$1\leq q\leq\alpha < \infty. \left\{(L^{q}, l^{p})^{\alpha}(\mathbb{R}^d):\alpha\leq p\leq\infty \right\}$$$ is a nondecreasing family of Banach spaces such that the Lebesgue space is $$$L^{\alpha}(\mathbb{R}^d)$$$ its minimal element and the classical Morrey space $$$\mathcal{M}_{q}^{\alpha}(\mathbb{R}^d)$$$ is its maximal element. In this note we investigate some closed linear subspaces of $$$(L^{q}, l^{p})^{\alpha}(\mathbb{R}^d)$$$. We give a characterization of the closure in $$$(L^{q}, l^{p})^{\alpha}(\mathbb{R}^d)$$$ of the set of all its compactly supported elements and study the action of some classical operators on it. We also describe the closure in $$$(L^{q}, l^{p})^{\alpha}(\mathbb{R}^d)$$$ of the set $$$\mathcal{C}_{\rm{c}}^{\infty}(\mathbb{R}^d)$$$ of all infinitely differentiable and compactly supported functions on $$$\mathbb{R}^{d}$$$ as an intersection of other linear subspaces of $$$(L^{q}, l^{p})^{\alpha}(\mathbb{R}^d)$$$ and obtain the weak density of $$$\mathcal{C}_{\rm{c}}^{\infty}(\mathbb{R}^d)$$$ in some of these subspaces. We establish a necessary condition on a function $$$f$$$ in order that its Riesz potential $$$I_{\gamma}(|f|) \;(0<\gamma<1)$$$ be in a given Lebesgue space. 
DO  - 10.21494/ISTE.OP.2023.0980 
JF  - Avancées en Mathématiques Pures et Appliquées 
KW  - Closed linear subspaces,  Approximation,  Adams-Spanne type theorem,  Riesz potential,  Fractional maximal operator, Closed linear subspaces,  Approximation,  Adams-Spanne type theorem,  Riesz potential,  Fractional maximal operator,  
L1  - http://openscience.fr/IMG/pdf/iste_apam23v14n3_3.pdf 
LA  - fr 
PB  - ISTE OpenScience 
DA  - 2023/06/15 
SN  - 1869-6090 
TT  - Characterization of some closed linear subspaces of Morrey spaces and approximation 
UR  - http://openscience.fr/Caracterisation-de-sous-espaces-vectoriels-fermes-des-espaces-de-Morrey-et 
IS  - Numéro 3 (Juin 2023) 
VL  - 14 
ER  -