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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 4, Pages 207–223 (Mi izv8026)  

This article is cited in 5 scientific papers (total in 5 papers)

Boundedness of integral operators in weighted Sobolev spaces

R. Oinarov

L. N. Gumilev Eurasian National University, Astana

Abstract: We obtain criteria for some classes of integral operators of Volterra type to be bounded operators from one weighted Sobolev space into another weighted Sobolev space.

Keywords: integral operators, weighted Lebesgue space, weighted Sobolev space, boundedness.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 1529/ГФ


DOI: https://doi.org/10.4213/im8026

Full text: PDF file (523 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2014, 78:4, 836–853

Bibliographic databases:

UDC: 517.51
MSC: 26D10, 45D05, 47B38, 47G10
Received: 02.07.2012
Revised: 11.03.2013

Citation: R. Oinarov, “Boundedness of integral operators in weighted Sobolev spaces”, Izv. RAN. Ser. Mat., 78:4 (2014), 207–223; Izv. Math., 78:4 (2014), 836–853

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov operators and duality principle in weighted Sobolev spaces of the first order”, Dokl. Math., 97:3 (2018), 232–235  mathnet  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
    2. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Spaces associated with weighted Sobolev spaces on the real line”, Dokl. Math., 98:1 (2018), 373–376  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
    3. V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis”, Math. Notes, 105:1 (2019), 91–103  mathnet  crossref  crossref  isi  elib
    4. Kalybay A., Oinarov R., “Kernel Operators and Their Boundedness From Weighted Sobolev Space to Weighted Lebesgue Space”, Turk. J. Math., 43:1 (2019), 301–315  crossref  isi
    5. Kalybay A., Oinarov R., Temirkhanova A., “Integral Operators With Two Variable Integration Limits on the Cone of Monotone Functions”, J. Math. Inequal., 13:1 (2019), 1–16  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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