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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 575–585
DOI: https://doi.org/10.4213/mzm8786 (Mi mzm8786) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the Regularization of a Multidimensional Integral Equation in Lebesgue Spaces with Variable Exponent

S. G. Samkoa, S. M. Umarkhadzhievb

a University of Algarve
b Chechen State University
Full-text PDF (531 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm8786
Abstract: A multidimensional integral equation of the first kind with potential-type kernel of small order in spaces of summable functions of variable order is reduced to an equation of the second kind.
Keywords: multidimensional integral equation of the first (second) kind, regularization of an integral equation, Lebesgue space with variable exponent, Banach space, hypersingular operator, Hölder's inequality, Hardy–Stein–Weiss inequality.
Received: 27.05.2010
Revised: 15.12.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 583–592
DOI: https://doi.org/10.1134/S0001434613030279
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: S. G. Samko, S. M. Umarkhadzhiev, “On the Regularization of a Multidimensional Integral Equation in Lebesgue Spaces with Variable Exponent”, Mat. Zametki, 93:4 (2013), 575–585; Math. Notes, 93:4 (2013), 583–592
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v93/i4/p575
    • This publication is cited in the following 3 articles:
    1. V. I. Burenkov, T. V. Tararykova, “On Holder's Inequality in Lebesgue Spaces with Variable Order of Summability”, J Math Sci, 278:2 (2024), 254  crossref
    2. Alexandre Almeida, Zalina A. Kusraeva, Humberto Rafeiro, “PROFESSOR STEFAN G. SAMKO RESEARCH: A DECADE RETROSPECTIVE”, J Math Sci, 266:3 (2022), 510  crossref
    3. V. I. Burenkov, T. V. Tararykova, “O neravenstve Geldera v lebegovykh prostranstvakh s peremennym poryadkom summiruemosti”, Posvyaschaetsya 70-letiyu prezidenta RUDN V.M. Filippova, SMFN, 67, no. 3, Rossiiskii universitet druzhby narodov, M., 2021, 472–482  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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