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Sbornik: Mathematics, 2017, Volume 208, Issue 1, Pages 44–59
DOI: https://doi.org/10.1070/SM8636 (Mi sm8636) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Approximation of functions and their conjugates in variable Lebesgue spaces

S. S. Volosivets

Saratov State University
English version PDF (511 kB) Citations (21)
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DOI: https://doi.org/10.1070/SM8636
Abstract: One-sided Steklov means are used to introduce moduli of continuity of natural order in variable $L^{p(\cdot)}_{2\pi}$-spaces. A direct theorem of Jackson-Stechkin type and an inverse theorem of Salem-Stechkin type are given. Similar results are obtained for the conjugate functions.
Bibliography: 24 titles.
Keywords: variable Lebesgue space, variable Sobolev space, $K$-functional, generalized modulus of continuity, direct and inverse approximation theorems, conjugate function.
Received: 18.11.2015 and 19.04.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 1, Pages 48–64
DOI: https://doi.org/10.4213/sm8636
Bibliographic databases:
Document Type: Article
UDC: 517.518.832
MSC: Primary 41A10, 41A17; Secondary 26A15, 26A16
Language: English
Original paper language: Russian
Citation: S. S. Volosivets, “Approximation of functions and their conjugates in variable Lebesgue spaces”, Mat. Sb., 208:1 (2017), 48–64; Sb. Math., 208:1 (2017), 44–59
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:74
    First page:63
     
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