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Tr. Mat. Inst. Steklova, 2001, Volume 232, Pages 298–317
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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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Proceedings of the Steklov Institute of Mathematics, 2001, 232, 290–309
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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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\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}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 290--309
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This publication is cited in the following articles:
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D. V. Prokhorov, V. D. Stepanov, “Weighted Estimates for the Riemann–Liouville Operators and Applications”, Proc. Steklov Inst. Math., 243 (2003), 278–301
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E. N. Lomakina, “Estimates for the approximation numbers of one class of integral operators. I”, Siberian Math. J., 44:1 (2003), 147–159
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E. N. Lomakina, “Estimates for the approximation numbers of one class of integral operators. II”, Siberian Math. J., 44:2 (2003), 298–310
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D. V. Prokhorov, “Weighted estimates for the Riemann–Liouville operators with variable limits”, Siberian Math. J., 44:6 (2003), 1049–1060
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Stepanov V.D., Ushakova E.P., “On integral operators with variable domains of integration”, Dokl. Math., 68:3 (2003), 409–413
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Maz'ya V., “Conductor inequalities and criteria for Sobolev type two–weight imbeddings”, Journal of Computational and Applied Mathematics, 194:1 (2006), 94–114
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R. Oinarov, “Boundedness and compactness of Volterra type integral operators”, Siberian Math. J., 48:5 (2007), 884–896
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V. D. Stepanov, E. P. Ushakova, “On the Geometric Mean Operator with Variable Limits of Integration”, Proc. Steklov Inst. Math., 260 (2008), 254–278
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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
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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
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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
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Ushakova E.P., “On boundedness and compactness of a certain class of kernel operators”, J Funct Spaces Appl, 9:1 (2011), 67–107
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R. Oǐnarov, “Boundedness and compactness in weighted Lebesgue spaces of integral operators with variable integration limits”, Siberian Math. J., 52:6 (2011), 1042–1055
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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
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Farsani S.M., “On the Boundedness and Compactness of a Certain Integral Operator”, Banach J. Math. Anal., 7:2 (2013), 86–102
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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
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Ushakova E.P., “Boundedness Criteria For the Hardy-Steklov Operator Expressed in Terms of a Fairway Function”, Dokl. Math., 91:2 (2015), 197–198
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M. G. Nasyrova, E. P. Ushakova, “Hardy–Steklov operators and Sobolev-type embedding inequalities”, Proc. Steklov Inst. Math., 293 (2016), 228–254
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R. Oinarov, “Boundedness and compactness of a class of convolution integral operators of fractional integration type”, Proc. Steklov Inst. Math., 293 (2016), 255–271
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D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112
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Oinarov R. Kalybay A., “Weighted Estimates of a Class of Integral Operators with Three Parameters”, J. Funct. space, 2016, 1045459
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Prokhorov D.V. Stepanov V.D. Ushakova E.P., “On weighted Sobolev spaces on the real line”, Dokl. Math., 93:1 (2016), 78–81
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E. P. Ushakova, “Alternative boundedness characteristics for the Hardy–Steklov operator”, Eurasian Math. J., 8:2 (2017), 74–96
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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
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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
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P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637
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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
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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
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