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 Mat. Zametki, 2014, Volume 95, Issue 4, Pages 492–506 (Mi mz9334)

On the Structural Properties of the Weight Space $L_{p(x),\omega}$ for $0< p(x)<1$

R. A. Bandaliev

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku

Abstract: 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, quasi-Banach space.

DOI: https://doi.org/10.4213/mzm9334

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English version:
Mathematical Notes, 2014, 95:4, 450–462

Bibliographic databases:

Document Type: Article
UDC: 517.518
Revised: 28.01.2013

Citation: R. A. Bandaliev, “On the Structural Properties of the Weight Space $L_{p(x),\omega}$ for $0< p(x)<1$”, Mat. Zametki, 95:4 (2014), 492–506; Math. Notes, 95:4 (2014), 450–462

Citation in format AMSBIB
\Bibitem{Ban14} \by R.~A.~Bandaliev \paper On the Structural Properties of the Weight Space~$L_{p(x),\omega}$ for $0< p(x)<1$ \jour Mat. Zametki \yr 2014 \vol 95 \issue 4 \pages 492--506 \mathnet{http://mi.mathnet.ru/mz9334} \crossref{https://doi.org/10.4213/mzm9334} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3298902} \elib{http://elibrary.ru/item.asp?id=21826473} \transl \jour Math. Notes \yr 2014 \vol 95 \issue 4 \pages 450--462 \crossref{https://doi.org/10.1134/S0001434614030171} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000335457300017} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899700085} 

• http://mi.mathnet.ru/eng/mz9334
• https://doi.org/10.4213/mzm9334
• http://mi.mathnet.ru/eng/mz/v95/i4/p492

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Bandaliev R.A., “Two-Weight Criteria For the Multidimensional Hardy-Type Operator in P-Convex Banach Function Spaces and Some Applications”, Ukr. Math. J., 67:3 (2015), 357–371
2. Chaichenko S., “Approximations of periodic functions by analogue of Zygmund sums in the spaces $L^{p(\cdot)}$”, Publ. Inst. Math.-Beograd, 99:113 (2016), 155–163
3. R. A. Bandaliev, S. G. Hasanov, “On venseness of $C_0^\infty(\Omega)$ and compactness in $L_{p(x)}(\Omega)$ for $0<p(x)<1$”, Mosc. Math. J., 18:1 (2018), 1–13
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