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Sibirsk. Mat. Zh., 2007, Volume 48, Number 5, Pages 1100–1115 (Mi smj1793)  

This article is cited in 16 scientific papers (total in 16 papers)

Boundedness and compactness of Volterra type integral operators

R. Oinarov

L. N. Gumilev Eurasian National University

Abstract: We introduce some nested classes of Volterra type integral operators. For the operators of these classes we establish criteria for boundedness and compactness in Lebesgue spaces.

Keywords: integral operator, Volterra type integral operator, operator of fractional integration, boundedness, compactness.

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English version:
Siberian Mathematical Journal, 2007, 48:5, 884–896

Bibliographic databases:

UDC: 517.518
Received: 08.12.2005
Revised: 19.05.2007

Citation: R. Oinarov, “Boundedness and compactness of Volterra type integral operators”, Sibirsk. Mat. Zh., 48:5 (2007), 1100–1115; Siberian Math. J., 48:5 (2007), 884–896

Citation in format AMSBIB
\by R.~Oinarov
\paper Boundedness and compactness of Volterra type integral operators
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 5
\pages 1100--1115
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 5
\pages 884--896

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    This publication is cited in the following articles:
    1. Oinarov R., Persson L.-E., Temirkhanova A., “Weighted inequalities for a class of matrix operators: the case $p\leqslant q$”, Math. Inequal. Appl., 12:4 (2009), 891–903  zmath  isi  elib
    2. 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
    3. 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
    4. L. S. Arendarenko, R. Oinarov, L.-E. Persson, “On the boundedness of some classes of integral operators in weighted Lebesgue spaces”, Eurasian Math. J., 3:1 (2012), 5–17  mathnet  mathscinet  zmath
    5. A. M. Abylayeva, A. O. Baiarystanov, “Compactness criterion for fractional integration operator of infinitesimal order”, Ufa Math. J., 5:1 (2013), 3–10  mathnet  crossref  mathscinet  elib
    6. R. Oinarov, “Boundedness of integral operators in weighted Sobolev spaces”, Izv. Math., 78:4 (2014), 836–853  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Kalybay A., Persson L.-E., Temirkhanova A., “a New Discrete Hardy-Type Inequality With Kernels and Monotone Functions”, J. Inequal. Appl., 2015, 321  crossref  mathscinet  zmath  isi  elib  scopus
    8. Abylayeva A., “Weighted Estimates For the Integral Operator With a Logarithmic Singularity”, International Conference on Analysis and Applied Mathematics (Icaam 2016), AIP Conference Proceedings, 1759, eds. Ashyralyev A., Lukashov A., Amer Inst Physics, 2016, 020043  crossref  isi
    9. Kufner A., Persson L.-E., Samko N., “Hardy Type Inequalities With Kernels: the Current Status and Some New Results”, Math. Nachr., 290:1 (2017), 57–65  crossref  mathscinet  zmath  isi  scopus
    10. Abylayeva A.M., Baiarystanov A.O., Persson L.-E., Wall P., “Additive Weighted l-P Estimates of Some Classes of Integral Operators Involving Generalized Oinarov Kernels”, J. Math. Inequal., 11:3 (2017), 683–694  crossref  mathscinet  zmath  isi  scopus
    11. Abylayeva A.M. Persson L.-E., “Hardy Type Inequalities and Compactness of a Class of Integral Operators With Logarithmic Singularities”, Math. Inequal. Appl., 21:1 (2018), 201–215  crossref  mathscinet  zmath  isi  scopus
    12. A. A. Kalybay, R. Oinarov, “Bounds for a class of quasilinear integral operators on the set of non-negative and non-negative monotone functions”, Izv. Math., 83:2 (2019), 251–272  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. A. A. Kalybay, “Weighted estimates for a class of quasilinear integral operators”, Siberian Math. J., 60:2 (2019), 291–303  mathnet  crossref  crossref  isi  elib
    14. A. A. Kalybay, Zh. A. Keulimzhayeva, R. Oinarov, “On a Kudryavtsev type function space”, Eurasian Math. J., 10:4 (2019), 34–46  mathnet  crossref
    15. Otelbaev M., Sultanaev Ya.T., Zhusupova D.S., “Criterion For the Boundedness and Compactness of a Class of Sets in l[0,Infinity)”, Differ. Equ., 55:9 (2019), 1258–1261  crossref  mathscinet  zmath  isi  scopus
    16. 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  mathscinet  zmath  isi  scopus
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