Geodesic
On Integral Operators with Variable Limits of Integration
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 298-317

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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. 
@article{TM_2001_232_a24,
     author = {V. D. Stepanov and E. P. Ushakova},
     title = {On {Integral} {Operators} with {Variable} {Limits} of {Integration}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {298--317},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_232_a24/}
}
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V. D. Stepanov; E. P. Ushakova. On Integral Operators with Variable Limits of Integration. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 298-317. http://geodesic.mathdoc.fr/item/TM_2001_232_a24/