Geodesic
Boundedness and compactness of a~class of convolution integral operators of fractional integration type
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 263-279

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For a class of convolution integral operators whose kernels may have integrable singularities, boundedness and compactness criteria in weighted Lebesgue spaces are obtained. 
@article{TM_2016_293_a17,
     author = {R. Oinarov},
     title = {Boundedness and compactness of a~class of convolution integral operators of fractional integration type},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {263--279},
     publisher = {mathdoc},
     volume = {293},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_293_a17/}
}
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R. Oinarov. Boundedness and compactness of a~class of convolution integral operators of fractional integration type. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 263-279. http://geodesic.mathdoc.fr/item/TM_2016_293_a17/