Geodesic
On the Structural Properties of the Weight Space~$L_{p(x),\omega}$ for $0 p(x)1$
Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 492-506

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The main purpose of this paper is to study the weight space $L_{p(x),\omega}$ for $0 p(x)\nobreak 1$ as well as the topology of this space. Embeddings between different Lebesgue spaces with variable exponent of summability are established. In particular, it is proved that the set of all linear continuous functionals over $L_{p(x),\omega}$ for $0 p(x)\nobreak 1$ consists only of the zero functional.
Keywords: weight space $L_{p(x),\omega}$, Lebesgue space with variable exponent of summability, embedding theorem, Lebesgue measurable function, quasinormed space
Mots-clés : quasi-Banach space. 
@article{MZM_2014_95_4_a1,
     author = {R. A. Bandaliev},
     title = {On the {Structural} {Properties} of the {Weight} {Space~}$L_{p(x),\omega}$ for $0< p(x)<1$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {492--506},
     publisher = {mathdoc},
     volume = {95},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a1/}
}
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R. A. Bandaliev. On the Structural Properties of the Weight Space~$L_{p(x),\omega}$ for $0< p(x)<1$. Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 492-506. http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a1/