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Tr. Mat. Inst. Steklova, 2001, Volume 232, Pages 298–317 (Mi tm221)  

This article is cited in 28 scientific papers (total in 28 papers)

On Integral Operators with Variable Limits of Integration

V. D. Stepanov, E. P. Ushakova

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: Integral Hardy-type operators with variable limits of integration are studied. For these operators, the boundedness and compactness criteria are obtained and applications are considered to the embeddings of the weighted Sobolev spaces on a half-axis into the Lebesgue spaces.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 290–309

Bibliographic databases:
UDC: 517.51
Received in October 2000

Citation: V. D. Stepanov, E. P. Ushakova, “On Integral Operators with Variable Limits of Integration”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 232, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 298–317; Proc. Steklov Inst. Math., 232 (2001), 290–309

Citation in format AMSBIB
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\by V.~D.~Stepanov, E.~P.~Ushakova
\paper On Integral Operators with Variable Limits of Integration
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 298--317
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm221}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851457}
\zmath{https://zbmath.org/?q=an:1007.46036}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 290--309


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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. D. V. Prokhorov, V. D. Stepanov, “Weighted Estimates for the Riemann–Liouville Operators and Applications”, Proc. Steklov Inst. Math., 243 (2003), 278–301  mathnet  mathscinet  zmath
    2. E. N. Lomakina, “Estimates for the approximation numbers of one class of integral operators. I”, Siberian Math. J., 44:1 (2003), 147–159  mathnet  crossref  mathscinet  zmath  isi  elib
    3. E. N. Lomakina, “Estimates for the approximation numbers of one class of integral operators. II”, Siberian Math. J., 44:2 (2003), 298–310  mathnet  crossref  mathscinet  zmath  isi
    4. D. V. Prokhorov, “Weighted estimates for the Riemann–Liouville operators with variable limits”, Siberian Math. J., 44:6 (2003), 1049–1060  mathnet  crossref  mathscinet  zmath  isi
    5. Stepanov V.D., Ushakova E.P., “On integral operators with variable domains of integration”, Dokl. Math., 68:3 (2003), 409–413  mathnet  mathscinet  isi
    6. Maz'ya V., “Conductor inequalities and criteria for Sobolev type two–weight imbeddings”, Journal of Computational and Applied Mathematics, 194:1 (2006), 94–114  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. R. Oinarov, “Boundedness and compactness of Volterra type integral operators”, Siberian Math. J., 48:5 (2007), 884–896  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. V. D. Stepanov, E. P. Ushakova, “On the Geometric Mean Operator with Variable Limits of Integration”, Proc. Steklov Inst. Math., 260 (2008), 254–278  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. Stepanov V.D., Ushakova E.P., “Weight estimates for norms of operators with two variable limits of integration”, Doklady Mathematics, 78:1 (2008), 541–543  crossref  mathscinet  zmath  isi  elib  scopus
    10. Stepanov V.D., Ushakova E.P., “On Boundedness of a Certain Class of Hardy–Steklov Type Operators in Lebesgue Spaces”, Banach Journal of Mathematical Analysis, 4:1 (2010), 28–52  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Stepanov V.D., Ushakova E.P., “Kernel Operators with Variable Intervals of Integration in Lebesgue Spaces and Applications”, Mathematical Inequalities & Applications, 13:3 (2010), 449–510  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Ushakova E.P., “On boundedness and compactness of a certain class of kernel operators”, J Funct Spaces Appl, 9:1 (2011), 67–107  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. R. Oǐnarov, “Boundedness and compactness in weighted Lebesgue spaces of integral operators with variable integration limits”, Siberian Math. J., 52:6 (2011), 1042–1055  mathnet  crossref  mathscinet  isi
    14. Oinarov R., “Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space”, Complex Variables and Elliptic Equations, 56:10–11 (2011), 1021–1038  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Farsani S.M., “On the Boundedness and Compactness of a Certain Integral Operator”, Banach J. Math. Anal., 7:2 (2013), 86–102  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. Eveson S.P., Stepanov V.D., Ushakova E.P., “a Duality Principle in Weighted Sobolev Spaces on the Real Line”, Math. Nachr., 288:8-9 (2015), 877–897  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. Ushakova E.P., “Boundedness Criteria For the Hardy-Steklov Operator Expressed in Terms of a Fairway Function”, Dokl. Math., 91:2 (2015), 197–198  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. M. G. Nasyrova, E. P. Ushakova, “Hardy–Steklov operators and Sobolev-type embedding inequalities”, Proc. Steklov Inst. Math., 293 (2016), 228–254  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    19. R. Oinarov, “Boundedness and compactness of a class of convolution integral operators of fractional integration type”, Proc. Steklov Inst. Math., 293 (2016), 255–271  mathnet  crossref  crossref  mathscinet  isi  elib
    20. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112  mathnet  crossref  crossref  zmath  isi  elib
    21. Oinarov R. Kalybay A., “Weighted Estimates of a Class of Integral Operators with Three Parameters”, J. Funct. space, 2016, 1045459  crossref  mathscinet  zmath  isi  elib  scopus
    22. Prokhorov D.V. Stepanov V.D. Ushakova E.P., “On weighted Sobolev spaces on the real line”, Dokl. Math., 93:1 (2016), 78–81  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    23. E. P. Ushakova, “Alternative boundedness characteristics for the Hardy–Steklov operator”, Eurasian Math. J., 8:2 (2017), 74–96  mathnet  mathscinet
    24. 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  crossref  crossref  zmath  isi  elib  elib  scopus
    25. 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
    26. P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    27. 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
    28. 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
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